The 35-year-old scored seven goals in 17 appearances last season after arriving at Fratton Park on New Year's Eve.
Connolly told Pompey's website: "This is a cracking club - I said that when I joined. There are a lot of good people here, I was made to feel very welcome and the fans took to me.
"I enjoyed my football last season and this is now a new era for the club - I'm happy to be a part of that. I've met the chief executive and he was very passionate about taking the club forward."
Former Watford, Wimbledon and West Ham frontman Connolly could also get the chance to help out on the coaching side.
Manager Guy Whittingham said: "It's a great deal for us. David's a dedicated professional footballer and a good influence for our younger players - on and off the pitch.
"Coaching is something he's interested in and it's fantastic if he can help with that, but first and foremost he's come back here to play."