As previously reported West Ham and Besiktas had been locked in talks over the transfer of Tore for weeks but had failed to agree upon a fee.
Besiktas wanted a €15 million upfront transfer fee for Tore but the Hammers were keen on a loan move.
The two clubs finally agreed terms on a loan deal with a €3 million fee paid to Besiktas and a €13 million buyout clause option.
Tore is currently on holiday and is expected to undergo his West Ham medical over the next few days before putting pen-to-paper.
The Turkish international winger worked with West Ham boss Slaven Bilic for two-seasons during his time in charge of Besiktas.
Tore scored his first league goal under the stewardship of Bilic at Besiktas and established himself as one of the most sought after players in the league.