The fusion of the BCR and ABL genes occurs due to a genetic event known as the Philadelphia chromosome translocation, specifically denoted as t(9;22)(q34;q11). During this translocation, a portion of chromosome 9 (where the ABL gene resides) is swapped with a portion of chromosome 22 (where the BCR gene resides). This leads to the creation of the BCR-ABL fusion gene on the altered chromosome 22.