“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.”
Rizespor have already started printing club shirts with the two players name and number on the back in anticipation of the transfer.
Adebayor and Flamini have flirted with moves to Turkish giants Galatasaray in the past but could end up league minnows instead.
The Black Sea based outfit are an ambitious club but there is no doubting their minnow status in comparison to the likes of the Istanbul giants or even nearby Trabzonspor.
The duo will become the latest former Premier League stars to move to the Turkish Super Lig.
Nani, Ozyakup, Gokhan Tore and Martin Skrtel are just a few to have played in the Super Lig over the years.