The 30-year-old defender had been a free agent for a short period of time following his release by Crawley Town at the end of last season.
Speaking about his new addition, Luton boss John Still told the club's official website: "We were a bit bare at right-back last season because we couldn't find the right one. Now we've been able to bring in somebody of Paul's ability and experience which is fantastic. He'll be a good addition for us."
Meanwhile, Connolly added: "Luton was a club I earmarked to come to in the summer. It's probably only one of three clubs in the division I would sign for.
"It's one of the biggest clubs in the league so it's a no-brainer. I'm at the stage of my career where I wanted to be playing for a club that is moving in the right direction and not just sitting still."