“We reached an agreement in principle with both players,” Rizespor coach Hikmet Karaman told Anadolu Agency.
“They’ll come to Rize within a few days and the last step of negotiations are going to be done.
“This is down to everyone devotedly working to finish the deals, so I have to thank the board of directors and our president.”
Turkish sports newspaper Fanatik meanwhile reported that Flamini and Adebayor will earn £1.7 million per-season.
Per the source, Flamini and Adebayor will arrive in Rize for their medical over the next few days where they will become the highest paid player at the Black Sea based club.
Rizespor have already started printing club shirts with the two players name and number on the back in anticipation of the transfer.
Flamini scored 13 times and provided 10 assists in 242 appearances for Arsenal but was released by the club this summer following the end of his contract – something that probably did not go down well with his good friend Mesut Ozil.
Adebayor meanwhile previously played for Arsenal, their London rivals Tottenham and Crystal Palace.