The 25-year-old has signed a four-year on Wearside and is hoping that the move to the Stadium of Light will boost his chances of securing a place in Fabio Capello's plans for next summer's World Cup finals.
"Obviously the England squad is a goal but at the moment I want to concentrate on getting in the team at Sunderland and playing consistently well," Turner said.
"Then if that was to come along, great, but first and foremost I want to perform here at Sunderland."
"It's a great time to be here. The signings which have already been made show Sunderland want to move in the right direction and I want to be a part of that." The former Brentford player, who has become Sunderland's seventh signing this summer, is hoping that manager Steve Bruce can accelerate his development thanks to is managerial acumen and his trophy-laden days with Manchester United.
"A lot of things attracted me to Sunderland the facilities, the stadium, the training ground, the fan base," Turner added.
"But a big factor was the manager. Steve Bruce is a proven manager who played in my position as a player, and hopefully he can add to my game.
"He has a real pedigree and did a great job at Wigan. Now he's come here and brought in some exciting players; I'm delighted to be able to join that group." Turner, whose arrival coincided with the departure of Danny Collins to Stoke in a £2.75-million deal, was linked with a move to Liverpool earlier this summer but he has insisted that Sunderland was his ideal destination even though Bruce can not offer European football.
"I'm over the moon to be here and get everything tied up," he added.
"As soon as I knew of the interest there was only one place I wanted to go," the Lewisham-born player said.
"With the deadline coming up it all happened quite quickly after I found out Sunderland were interested. I played yesterday for Hull and now I'm pleased to be here.
"I've played at the Stadium of Light two or three times and it's an unbelievable place with a great atmosphere. It's one of my favourites.
"I'm just pleased I'll be getting the opportunity to play there every other week.