Inclusion Criteria:

          1. Male or female participants 18 years or older.

          2. Must have a histopathologically documented diagnosis of primary or secondary AML
             (excluding acute promyelocytic leukemia), as defined by World Health Organization
             (WHO) criteria (Jaffe et al, 2001), for whom no standard therapies are anticipated to
             result in a durable remission according to the clinical judgment of the principal
             investigator, or who refuses standard therapies (phase 1b and 2).

          3. Participants for the phase 2 portion of the study must, in addition, meet the
             following:

             o Must be refractory to or relapsed after no more than 2 prior chemotherapy regimens.
             Re-induction with the same regimen or stem cell transplant will not be considered a
             separate regimen.

          4. Eastern Cooperative Oncology Group performance status of 0 to 1.

          5. Female participants who:

               -  Are postmenopausal for at least 1 year before the screening visit, or

               -  Are surgically sterile, or

               -  If they are of childbearing potential, agree to practice 2 effective methods of
                  contraception, at the same time, from the time of signing the informed consent
                  through 180 days after the last dose of study drug, or

               -  Agree to practice true abstinence, when this is in line with the preferred and
                  usual lifestyle of the participant. (Periodic abstinence [example, calendar,
                  ovulation, symptothermal, postovulation methods], withdrawal, spermicides only,
                  and lactational amenorrhea are not acceptable methods of contraception. Female
                  and male condoms should not be used together).

             Male participants, even if surgically sterilized (that is, status postvasectomy), who:

               -  Agree to practice effective barrier contraception during the entire study
                  treatment period and through 180 days after the last dose of study drug, or

               -  Agree to practice true abstinence, when this is in line with the preferred and
                  usual lifestyle of the participant. (Periodic abstinence [example, calendar,
                  ovulation, symptothermal, postovulation methods for the female partner],
                  withdrawal, spermicides only, and lactational amenorrhea are not acceptable
                  methods of contraception. Female and male condoms should not be used together).

          6. Voluntary written consent must be given before performance of any study-related
             procedure not part of standard medical care, with the understanding that consent may
             be withdrawn by the participant at any time without prejudice to future medical care.

          7. In the absence of rapid progressive disease, the interval from prior systemic
             anticancer treatment to time of TAK-659 administration should be at least 2 weeks for
             cytotoxic agents (other than hydroxyurea), or at least 5 half-lives for noncytotoxic
             agents, and participants have to have recovered from acute toxicities of these
             therapies. Participants who are on hydroxyurea may be included in the study and may
             continue on hydroxyurea for the first 28 days while participating in this study.

          8. Suitable venous access for the study-required blood sampling, including
             pharmacokinteic (PK) and pharmacodynamic (PD) sampling and blood transfusion support.

          9. Clinical laboratory values as specified in the following:

               -  Total bilirubin must be less than or equal to (<=) 1.5* the upper limit of normal
                  (ULN).

               -  Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) must be
                  less than or equal to (<=) 2.5*the ULN.

               -  Lipase <=1.5*ULN and amylase <=1.5*ULN with no clinical symptoms suggestive of
                  pancreatitis or cholecystitis.

               -  Creatinine clearance greater than or equal to (>=) 60 milliliter per minute
                  (mL/min) either as estimated by the Cockcroft-Gault equation or based on urine
                  collection (12 or 24 hours).

        Exclusion Criteria:

          1. Clinically active central nervous system leukemia.

          2. Female participants who are lactating and breastfeeding or have a positive serum
             pregnancy test during the Screening period or a positive urine pregnancy test on Day 1
             before first dose of study drug.

          3. Any serious medical or psychiatric illness, including drug or alcohol abuse that
             could, in the investigator's opinion, potentially jeopardize the safety of the
             participant or interfere with the objectives of the study.

          4. Systemic anti-cancer treatment (including investigational agents) <=21 days or <=
             5*their half-lives before the first dose of study treatment. (For example, if the
             5*the half-life is shorter than 21 days, 5*half-life should be used as the washout
             period. However, a minimum of 10 days should elapse from prior therapy to initiating
             protocol therapy).

          5. Persistent clinically significant toxicity from prior chemotherapy that is Grade 2 or
             higher by the National Cancer Institute Common Terminology Criteria for Adverse Events
             (NCI CTCAE) (v4.03).

          6. Receipt of hematopoietic stem cell transplant (HSCT) within 60 days of the first dose
             of TAK-659; clinically significant graft-versus-host disease (GVHD) requiring ongoing
             immunosuppressive therapy post HSCT at the time of screening (use of topical steroids
             for ongoing skin GVHD is permitted).

          7. Active, systemic infection requiring intravenous (IV) antibiotic, antifungal, or
             antiviral therapy or other serious infection within 14 days before the first dose of
             study drug.

          8. Major surgery within 14 days before the first dose of study drug and have not
             recovered fully from any complications from surgery.

          9. Radiotherapy less than 2 weeks before the first dose of study treatment or have not
             recovered from acute toxic effects from radiotherapy.

         10. Known human immunodeficiency virus (HIV) positive (testing not required).

         11. Known hepatitis B surface antigen-positive, known or suspected active hepatitis C
             infection (testing not required).

         12. Evidence of currently uncontrolled cardiovascular conditions as listed in the
             protocol; acute myocardial infarction with 6 months before starting study drug;
             baseline QT interval (QTcF) greater than (>) 450 milliseconds (msec) (males) or > 475
             msec (females); or abnormalities on baseline 12-lead electrocardiogram (ECG) that are
             considered clinically significant per investigator.

         13. Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral
             absorption or tolerance of TAK-659 including difficulty swallowing tablets; diarrhea >
             Grade 1 despite supportive therapy.

         14. Use or consumption of any of the following substances:

               -  Medications or supplements that are known to be inhibitors of P-glycoprotein
                  (P-gp) or strong inhibitors or inducers of Cytochrome (CY) P3A within 5 times the
                  inhibitor half-life (if a reasonable half-life estimate is known) or within 7
                  days (if a reasonable half-life estimate is unknown) before the first dose of
                  study drug. In general, the use of these agents is not permitted during the study
                  except for AE management.

               -  Medications or supplements that are known to be strong CYP3A mechanism based
                  inhibitors or strong CYP3A inducers and/or P-gp inducers within 7 days or within
                  5 times the inhibitor or inducer half-life (whichever is longer) before the first
                  dose of study drug. In general, the use of these agents is not permitted during
                  the study except for AE management.

               -  Grapefruit-containing food or beverages within 5 days before the first dose of
                  study drug. Note that grapefruit-containing food and beverages are not permitted
                  during the study.

         15. White blood cell count > 50,000 per micro liter (/µL); hydroxyurea may be used to
             control the level of circulating leukemic blast cell counts prior to study entry and,
             if needed, concomitantly while on TAK-659 treatment during the first 28 days of the
             study. Hydroxyurea can be used up to a maximum dose of 5 gram per (g/) day.