Rosenior helped Hull secure promotion from the Championship last season and will remain at the KC Stadium until 2015.
The 28-year-old has previously played in the top-flight with Fulham and Reading and believes he can still hold his own against the top attacking talent in the country.
"I've been waiting for four or five years to get back to the Premier League and prove that I can play at that level," said Rosenior.
"If I can get the chance, I want to prove to everyone and also to myself that I'm good enough to play well in this league and help the club to get results.
"Because we've come up from the Championship, we will be viewed as underdogs but I think we can use that to our advantage.
"Having the opportunity to play in the Premier League again is one that I want to take and I'm very much looking forward to it."
New defensive recruits Curtis Davies and Maynor Figueroa could line-up with Rosenior in Hull's rearguard and he expects them to make a big impact next season.
"The manager is building a good squad," said Rosenior.
"We've got a lot of good players here, a lot of underrated players and a young squad, one that I think will get better together.
"The players that we've signed so far this summer will add to what we've already got. I've known Curtis Davies for 10 years and I played with him for England U21s - he's a fantastic centre half and he'll fit in fantastically well here.
"We've also brought in Maynor Figueroa who is one of the best left backs in the Premier League and I think it is a real coup for us to sign him.
"Add all of that to what we've already got and it's looking good for the new season. I'm delighted to be here and hopefully we can keep this club progressing and moving forward."