The 28-year-old, who joined West Ham United in a record transfer fee of £20.5 million from Swansea in 2016, suffered a hamstring injury on his debut game against Chelsea and later returned to the Welsh side after falling down the pecking order in David Moyes' setup.
"Ayew today left the Swans' pre-season tour in Austria to travel to Turkey for a medical ahead of his move to the Super Lig, which will be completed subject to international clearance," a club's statement read.
"The Turkish giants will also have the option to purchase Ayew on a permanent deal at the end of his loan spell," the statement added.
Swansea coach Graham Potter, who recently replaced Carlos Calvahal, lauded Ayew's attitude during pre-season.
“I understand the circumstances of the move – it’s part of the restructure of us going forward,” he said.
“From my perspective, he has been brilliant. He has applied himself in training, supported what we are trying to do and been very professional.
“He has been a joy to work with and we wish him the best,” he added.
Ayew becomes the latest Ghanaian to don the jersey of Fenerbahce after former Black Stars captain Stephen Appiah and Sam 'Foyoo' Johnson.