Masuaku, who joined the Hammers from Olympiacos in 2016, will spend the season with the Turkish club and the deal includes an option to make the switch permanent.
The 28-year-old made only six Premier League starts last term and would have slipped further down the pecking order should Moyes succeed in bringing in competition for Aaron Cresswell.
The Hammers have been in talks with Eintracht Frankfurt over a deal for their No1 target, Serbian wing-back Filip Kostic, and are willing to meet the German club’s asking price - but convincing the player to make the move is proving more difficult.
After winning the Europa League last term, Frankfurt can offer Champions League football this season while Kostic has just one year on his contract and could therefore move on a lucrative free transfer next summer, with a number of leading Italian clubs reportedly keen.
The 29-year-old is, however, understood to be tempted by a move to London and the Hammers will continue to monitor the situation as the window progresses.
In the meantime, Moyes is keen to explore alternative options, with Masuaku’s departure leaving Cresswell as the Scot’s only natural left-back option, though Ben Johnson can deputise.