The spontaneously broken time reversal symmetry can lead to the formation of an energy gap in the Dirac spectrum of the surface states of a topological insulator (TI) which can consequently give rise to a variety of interesting phenomena potentially useful for spintronics. In this work, we couple a non-magnetic TI to a high Curie temperature TC magnetic insulator to induce strong exchange interaction via the proximity effect. We have successfully grown 5 quintuple layer thick ternary TI (BixSb1-x)2Te3 films on atomically flat yttrium iron garnet (YIG) film with the combination of molecular beam epitaxy and pulsed laser deposition, in which the Fermi level position relative to the Dirac point is varied by controlling the Bi:Sb ratio. The anomalous Hall effect (AHE) and suppressed weak antilocalization (WAL) measured under out of plane magnetic fields reveal that the TI surface in contact with YIG is magnetized. Our high-quality (BixSb1-x)2Te3/Y IG heterostructure provides a tunable system for exploring the quantum anomalous Hall effect (QAHE) at higher temperatures in TI-based spintronic devices.