The 25-year-old Trinidad & Tobago international ended a three-year stay at the Stadium of Light after Bruce accepted the Potters' club-record offer of £8million. As well as revealing his frustration with Jones' sporadic bursts of form, Bruce told the Sunderland Echo: "Towards the end with Kenwyne, things were not working out so I have accepted Stoke's offer.
"There has always been a frustration with me, and I think with supporters who have watched Kenwyne, that you see an abundance of talent but it has not come out often enough for us for whatever reason. In management you get paid to make some important decisions sometimes. Stoke have been badgering me for a year. Everyone knows they love a big, traditional centre-forward and he might go and suit them.''
Jones, who has signed a four-year deal, responded on Stoke Player: "Sometimes circumstances happen that you have to leave. It's never good to leave a place when you've been there for a while but I'm looking forward to doing well for Stoke.''
The former Southampton forward became a favourite at the Stadium of Light following a £6million move in 2007 and was named the club's player of the season the following summer. But Darren Bent seized the goalscoring mantle decisively following his arrival from Tottenham last year, netting 25 times, with Jones frequently finding himself on the bench.
Jones will now try to rediscover the form that previously attracted the likes of Tottenham and Liverpool at the Britannia Stadium, where he had a successful spell on loan in 2005. Stoke boss Tony Pulis has bided his time in the transfer marker, signing only two fringe players before Wednesday's deal, which surpassed the £6million paid to Middlesbrough for Robert Huth last summer as the club's biggest outlay.
Lee Cattermole will be Sunderland's new team captain following the departure of Lorik Cana this summer, with veteran Boudewijn Zenden taking on the role of club skipper.
"Lee epitomises everything a manager looks for in a team captain," Bruce said. "He always shows passion, pride and commitment to the cause, and never gives up. Lee shows the kind of 100% effort which Sunderland fans expect and are entitled to.
"Bolo has been a huge influence in the dressing room since he arrived, often acting as a link between the management and the players. Bolo is a fantastic mentor for our younger players.''