The 24-year-old said Hammers boss Slaven Bilic was "a big factor" in his move to the Olympic Stadium, adding: "He's the best manager I have played under."
"He [Bilic] is the main man and knows me very well. I could not have said 'no' to him," said the Cologne-born wide player.
"He is like a father to the players. You feel like you are family."
West Ham said Tore would prepare for the new season at the club's training ground while the rest of the first-team squad finish their pre-season tour of America.