Boruc, 33, was almost sacked by Saints after throwing a bottle into the home crowd during the 2-1 defeat by Tottenham in October.
The Poland international has fought his way back into the fans' good books since Mauricio Pochettino replaced Nigel Adkins as manager.
Boruc said: "The only way to get the fans behind you is to be a good player. I have worked hard and what happened is in the past.
"It was a bit of a roller coaster at the start but I am looking forward and I will do anything to make the club better.
"Clubs like Swansea have shown that by playing a totally different brand of football, you can achieve a lot. You need to be ambitious in your life."