The 26-year-old has penned an 18-month deal with the Shrimps, having joined Northampton Town last summer.
Connolly said: “I am buzzing to be here, I cannot wait to get going now.
“I know Martin Foyle (head of recruitment) from my time at Northampton, he knows me as a player and a person as well.
“My agent phoned me towards the end of last week and said that there was a bit of interest, and it has just snowballed from there really.
“We have managed to get everything done pretty quickly, if I am honest.
“I am excited about the move. The gaffer thinks I can play a big part in the way he wants the team to play, a style which will complement my game too.
“I know a few of the players from my time in football. I have lived with Shane (McLoughlin) in the past, I know Anthony (O’Connor) and Ryan (Delaney) as well.
“League One is a good standard and I am looking forward to testing myself at this level again.
“I will work really hard to earn myself a place in the team and I cannot wait to get started.”
Connolly’s career started with Bohemians before moves to Shelbourne and Ipswich Town.
Almost 100 appearances followed for Bray Wanderers and Dundalk before joining AFC Wimbledon for an undisclosed fee in January 2019.
He spent a year-and-a-half with the Dons, a spell which included a loan move to Bradford City, before joining St Mirren in 2020.
After making 39 appearances in league and cup, helping them to seventh place in the Scottish top flight, Connolly turned down a new deal and joined Northampton.
Robinson added: “Dylan is another player that I tried to sign in the summer, but unfortunately for us, he decided to sign for Northampton – but I have always been a big admirer.
“He adds something different to what we have here already. He has electric pace, is a dynamic wide player who gets balls into the box and he is a good character to have around the dressing room.
“I know him well from my time in Scotland when he was playing at St Mirren.
“I know Martin (Foyle) has a good relationship with him from their time at Northampton, so I am pleased to get everything done and dusted.”
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