The 26-year-old, whose transfer from Burnley was confirmed on Wednesday, is to compete with long-serving club captain Deeney for the central striker's role in new manager Marco Silva's 4-3-3.
Deeney has become a fans' favourite during his seven years at Watford, where he has been a consistent figure amid significant change.
However Gray, who revealed he had been tempted south by the prospect of playing in a more expansive team, knows he has been recruited to become his rival.
"It's down to me; it's competition like it would be anywhere," said Gray of his direct battle with the 29-year-old Deeney. "I've got to train well, work hard, and get myself into the team.
"However the manager wants to play, that's down to him and it's down to me to prove to him that I'm worthy of starting."