The 24-year-old, who passed through Chelsea's youth academy earlier in his career, joins the Hammers for the forthcoming campaign for a loan fee of £2.5million.
Tore played under West Ham boss Slaven Bilic at Besiktas and there is an option in place for the Premier League club to buy the Turkey international for a further £10million.
The former Hamburg man won Turkey's Super Lig last season and hailed father-figure Bilic as one of the reasons in him deciding to return to England.
"I am very happy to be at West Ham," he told the club's official website.
"I watched many games that they played last season and saw how passionate the fans are
That made me want to come here and I am looking forward to playing in front of them.
"Slaven was also a big factor in me coming here and he is a great manager
He is the main man and knows me very well
I could not have said no to him.
"He is the best manager I have worked under and he is like a father to the players
You feel like you are family."
The club confirmed Tore will not link up with the squad, who are currently on a pre-season tour of the United States, but will begin his build-up to the new season at their Chadwell Heath training base.
He is the third major summer recruit for Bilic ahead of West Ham's maiden season at the Olympic Stadium following the arrivals of midfielder Havard Nordtveit and Algerian international winger Sofiane Feghouli.
The Hammers began their pre-season with a 3-0 defeat to Seattle Sounders last week and face North American Soccer League outfit Carolina RailHawks on Wednesday before returning home.
Source : PA
Source: PA