The 27-year-old Wales international striker is believed to have signed a three-year deal, after joining for an undisclosed fee.
Jackett told the Southwark News: "Personally, I'd like to thank him for what he's done because he's done very well for the club over the last couple of seasons here.
"We haven't left it on bad terms and there are no issues at our end.
"We've tried very hard to keep Steve over the past six months, but we obviously have to look after the club along the way and make sure that the club's interests were in our thinking, especially in my position as the manager.
"So we wish Steve well in his future career and in the Premier League with Norwich."