The East London based club are reported to have reached an agreement after weeks of negotiations.
The Hammers are reported to have already agreed personal terms with Tore who wants to make the move a source close to the club told Turkish-football.com.
Besiktas president Fikret Orman recently revealed that West Ham had made a loan bid with a future buyout clause option which was rejected.
“We received a loan offer with a buyout clause option which we rejected,” Orman stated in his press-conference.
The Black Eagles are still under the watch of FFP and Orman revealed that they must continue to increase revenues.
“We have not transfer listed Gokhan Tore he is a very important player but if he wants to leave we will sell him for the right price,” he added.
Orman also confirmed that the Turkish international is available of the right price.
West Ham have been closely linked with Tore since last year. Hammers boss Slaven Bilic coached the explosive winger for two-seasons during his time in charge of the Black Eagles and is widely credited with developing him into one of the most highly sought after players in the league.