Nilotinib and Imatinib Mesylate After Donor Stem Cell Transplant in Treating Patients With ALL or CML

Inclusion Criteria: * Body surface area \>= 1 m\^2 * Allogeneic HCT * Acute lymphocytic leukemia (ALL) or chronic myelogenous leukemia (CML) characterized by the p190 and/or p210 BCR/ABL gene rearrangement * CML in accelerated phase, blast crisis, or blast crisis remission as defined by World Health Organization (WHO) criteria * CML in chronic phase if patient age =\< 17 years or a patient of any age with CML in second chronic phase or beyond * Patients with minimal residual disease (MRD) that is not declining in response to tyrosine kinase inhibitor therapy must be screened for the T315I and other mutations * An appropriately matched related or unrelated donor * Signed informed consent * Patient must have a life expectancy of at least 2 months * Stated willingness of the patient to comply with study procedures and reporting requirements * Creatinine =\< 2.0 x upper limit normal (ULN) * Platelets \> 20 x 10\^9 /L * Serum aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN, conjugated bilirubin \< 3 x ULN * Serum potassium phosphorus, magnesium, and calcium \>= lower limit normal (LLN) or correctable with supplements prior to first dose of study drug; calcium levels may be corrected for hypoalbuminemia * Serum amylase and lipase \< 1.5 x ULN * Female patients of childbearing potential must have negative pregnancy test within 7 days before initiation of study drug dosing; postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential; male and female patients of reproductive potential must agree to employ an effective barrier method of birth control throughout the study and for up to 3 months following discontinuation of study drug * Careful rationalization with a view to discontinuing or considering alternatives to any concomitant medications that have potential to prolong the QT interval Exclusion Criteria: * Autologous transplant * Non-myeloablative transplant * Patient age \> 17 years with CML in first chronic phase * Aberrant antigen expression on marrow leukemic blasts \>= 5% by multidimensional flow cytometric assay immediately before conditioning (CML patients in chronic phase exempt from flow cytometry screening) * Ph+ ALL without complete cytogenetic remission immediately before conditioning * Known T315I mutation * Hypersensitivity to Gleevec or Tasigna * Patients who are Tasigna-resistant or intolerant * Central nervous system (CNS) involvement with leukemia at baseline (pre-imatinib therapy); CML chronic phase (CP), accelerated phase (AP) patients exempt from CNS involvement screening * Female patients who are pregnant, breast-feeding, or of childbearing potential without a negative serum pregnancy test at screening; male or female patients of childbearing potential unwilling to use effective contraceptive precautions throughout the trial; post-menopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential * Life expectancy severely limited by diseases other than leukemia * Myocardial infarction within one year prior to starting nilotinib * Other clinically significant heart disease (e.g. congestive heart failure, uncontrolled hypertension, unstable angina) * Absolute neutrophil count (ANC) less than 1500 per microliter at study entry despite the use of filgrastim (G-CSF) * Impaired cardiac function, including any one of the following: * Complete left bundle branch block or bifascicular block (right bundle branch block plus left anterior hemiblock) or use of ventricular-paced pacemaker * Congenital long QT syndrome or a family history of long QT syndrome * History of or presence of significant ventricular or atrial tachyarrhythmias * Clinically significant resting bradycardia (\< 50 beats per minute) * Corrected QT interval (QTc) \> 450 milliseconds on screening electrocardiogram (ECG); if QTc \> 450 and electrolytes are not within normal ranges, electrolytes should be corrected and then the patient rescreened for QTc