The two clubs have agreed an undisclosed fee for the Robins 20-year-old striker and he is now set to begin talks with The Royals about a possible move.
"It's an exciting prospect because Reading are ambitious to make the Premiership and that is where I want to be," he told Readings official website.
"It's more about playing Championship football than money as far as I'm concerned.
"It's up to me now that an offer has been accepted. It's not an easy decision and I won't make the move if I don't think it's right.
"I'll have no problem staying where I am. I've had four years at Ashton Gate and have been very happy."