The Seagulls named former Barcelona midfielder Garcia as head coach after their controversial sacking of manager Gus Poyet last month.
Poyet brought Ulloa to the Amex in January and after reaching double figures the Argentinian frontman is looking forward to building on a successful introduction to English football.
"I'm very happy to have Oscar here and the way that everything is working," Ulloa told the club website.
"I didn't know him before but I have heard some good things about him from some other players that I've played with. People have been speaking very well about him.
"Last season went very well but that was last season and I'll start again from zero. I've prepared as well as possible to have a good season.
"I'd love to keep the same level as last season, and the season before that at Almeria. The more goals I score the better we will be playing as a team."