The 25-year-old has joined the Steelmen for an undisclosed fee, and has signed a two year contract with the club.
Levitt came through the ranks of Manchester United's academy, and is no stranger to the Scottish Premiership, having played for both Hibernian and Dundee United previously.
Manager Alfred Johansson said: "Dylan will be a player well-known to our support.
"We have recruited from leagues across the globe this summer, but bringing someone in who has ample experience in this division is also really important. Dylan has played almost 100 games in the Scottish Premiership, so he knows exactly what's needed.
"His ability on the ball and characteristics were exactly what we wanted, and we feel he bolsters our options in the middle of the pitch. We have some really strong players in this position who will all be pushing each other on throughout the season.
"I'm excited to see Dylan in our system and feel our summer recruitment has put the squad in a really healthy position."
Levitt added: "I feel like I should be able to slot in here quickly and easily. From the games I've watched this season, this is the perfect system for me to play in.
"There are some really good players in the building, and now it's my job to get to work and try to push into the team."