The 23-year-old spent the second half of last season at the MKM Stadium, where he made six appearances and scored two goals, both of which came in a victory over Queens Park Rangers.
Hull have now brought Connolly back to the club on a permanent basis, with the striker joining for an undisclosed fee.
"I'm delighted Aaron has joined us. He showed in a short time the impact he can have on not just the team but the group," manager Liam Rosenior told the club's official website.
"He wants to be here and show his true worth. I can't wait to get him fit and for him to fulfil his potential with us.
"Aaron represents everything I want on the pitch from my team: energy, pace, aggression and quality. He's not on loan; Aaron's one of us now. That's going to be important for Aaron as well and I'm delighted he's going to be part of us.
"What convinced me to sign him again was his determination to come here. He had interest from other clubs but discounted them because he wanted to be at this club.
"He believes we can get to where we want to be and I can't wait to see him back on the pitch."
Connolly leaves Brighton having made 52 Premier League appearances for the club, while he is also an eight-time Republic of Ireland international.
The forward becomes the Tigers' fourth signing of the summer - after Liam Delap, Jason Lokilo and Ruben Vinagre - and could make his second debut when they begin their new Championship campaign away to Norwich City on Saturday.