The 25-year-old Egypt international has signed a three-year deal after the two clubs agreed an undisclosed fee.
Sunderland confirmed the transfer via their official Twitter account, saying: "Ahmed Elmohamady has joined Hull City on a three-year deal for an undisclosed fee."
Elmohamady, who made 41 appearances on loan for the Tigers last season, was delighted to have been re-united on a permanent basis with manager Steve Bruce, who brought him to England during his spell in charge at the Stadium of Light.
He told Hull's official website: "It feels great to be here permanently, especially after what happened here last season. It was a great year and I thoroughly enjoyed playing for this club.
"Everything about it was great - the players, the staff, the fans - and I am delighted to be here again.
"It's going to be great to play in the Premier League again, especially with Hull City, and I am very much looking forward to the new season.
"Moving here was an easy decision to make. The fans are fantastic and it will be enjoyable to play in front of them in the Premier League."
Elmohamady first linked up with Bruce on Wearside after completing a loan move to Sunderland from ENPPI in August 2010, and he sealed a permanent £2million switch the following summer.
He said: "The manager was the one who brought me over from Egypt to play for Sunderland and now he has brought me here. I really enjoy playing for him and I look forward to doing so again now."
Having resolved his future, Elmohamady, who went away on international duty following the conclusion of the domestic campaign, will now enjoy a short holiday before returning to Humberside for pre-season training.
He said: "We have had World Cup qualifiers with Egypt. I will now have a few days off before I come back for pre-season training."