Gomis has signed a three-year deal with the Turkish Super Lig club, who are rebuilding their squad after finishing fourth in the table last season.
Galatasaray also confirmed Belhanda, who spent last season on loan at Ligue 1 side Nice, is nearing a move from Dynamo Kiev, while negotiations are ongoing with Sao Paulo over the signing of Brazilian defender Maicon.
The pair are expected to join Gomis at the club after the 31-year-old completed his switch from Swansea on Thursday, with the Frenchman thrilled by his latest move.
"First of all I am very happy to come to a big club like Galatasaray," Gomis said. "Not only in Turkey, but also in the world and Europe, a team that is recognised and successful.
"The welcome at the airport impressed me very much. It was a very warm welcome. I thank the Galatasaray supporters.
"There was a great desire to be a part of this team. They were constantly calling. I was very impressed with this."