The former Swindon keeper told the club website: "It's important I finished the season strongly and now I have the opportunity to carry that on next year.
"I've settled here with my girlfriend. I think Brighton is the nicest city in England and we're really happy here."
Albion boss Gus Poyet, who coached Brezovan at Swindon, added: "Peter has earned his new deal.
"Initially he came to play and help us out but I expected he would prove he was worth a longer deal and he has done that."
Source: BBC Sport
Source: BBC Sport