Gray led the line with 23 goals as Burnley won the Championship title last season, returning to the top flight at the first time of asking.
The 25-year-old striker only made his English Football League debut on 10 August 2014, after signing for Brentford from Luton Town in the National League.
But after 18 goals in 2014/15 and a title-winning debut campaign at Burnley, he has continued his prolific form by netting nine times in six pre-season appearances ahead of his Premier League debut, and Heaton, the club captain, is backing Gray to shine at the highest level.
"He has the qualities to succeed in the Premier League," Heaton said at the 2016/17 Premier League Season Launch. "Last season he came in, settled in quickly, scored lots of different goals.
"On the back of a successful season he's gone away and worked really hard, he’s in great shape. He's come back in pre-season on fire.
"Everything’s in place for him to have a fantastic season. The sky’s the limit with his qualities. He can cause defences a lot of problems and I’m backing him to score a lot of goals."
Gray's manager Sean Dyche believes Gray should be inspired by the rise of Leicester City striker Jamie Vardy from non-league to the 2015/16 Premier League title and Player of the Season award within four years.
"For Andre, Vardy can be an inspiration," Dyche said. "Andre's done fantastically well, not just last season but over the past three of four seasons on his journey to where he is now.
"He'll be an important player but so many others will be."