The 26-year-old, who arrived from Reading in late October on a short-term contract that was due to expire at the end of next week, believes Hull will continue to rise up the npower Championship table.
Rosenior said: "I'm delighted. It's something that we kind of half agreed when I first came here, but it relied on the takeover being completed for me to stay.
"I've really enjoyed my time here so far and to be honest I don't think there is anywhere I would rather be at the moment, especially in this league.
"We've got a good squad, good coaching staff and we've started to pick up results. There's also money to spend next month now.
"I could sense when I first joined that things hadn't been going too well, but I looked at the squad and it's one of the best in the division in my opinion."