The 18-year-old headed for Wearside on Tuesday night to undergo a medical after the Black Cats' offer of £8.1million, potentially rising to £12million, was accepted.
Talks over a four-year contract have now been concluded with Bruce having got his man after striking decisively to land a player who had previously been linked with Liverpool - the club he supported as a boy - Arsenal and Tottenham.
Bruce said: "A number of top sides have been chasing Connor for some time now, so naturally we are absolutely delighted he has chosen to come to Sunderland.
"He's still very young, but at 6ft 3in he's a physical presence. With his height and style of play, he will offer us a threat in front of goal and complement our existing strikers.
"We have been watching him for a while now and he is improving and developing all the time. He's a great prospect and I'm sure our supporters will love watching him play."
The Hereford-born England Under-21 international emerged from the ranks at Portman Road to establish himself in the first team. He scored nine npower Championship goals last season.
He is unlikely to be the last striker to arrive at the Stadium of Light this summer with Bruce targeting at least two, if not three, frontmen following a difficult end to the last Premier League campaign.
The Black Cats took the decisions to accept Aston Villa's £24million bid for leading scorer Darren Bent in January and not to spend in haste to replace him with Fraizer Campbell close to a return from a knee injury.
However, with loan signing Danny Welbeck, who has since returned to parent club Manchester United, also sidelined, Campbell broke down in training and will miss most of next season as well.
That left Asamoah Gyan as the club's only fit senior specialist up front, and that is a situation Bruce is desperate to address as a matter of urgency.
South Korea international Ji Dong-won is close to completing his move from Chunnam Dragons, while much of the groundwork on a deal to bring Liverpool's David Ngog to Wearside has been done, although his arrival is less certain.