The 20-year-old, who is yet to make his AFL debut, spent two years with the Swans but was unable to break into the starting line-up.
Dick, a 187cm defender, uses his pace to his advantage and has the ability to burst through the middle of the ground.
He was selected by the Swans with pick No.64 in the 2012 NAB AFL Draft after playing 14 games in the TAC Cup with the Calder Cannons.
Blues general manager of football operations Andrew McKay said Dick would strengthen the team’s backline and midfield next season.
“It’s great to get a versatile young player like Matthew through the door, particularly coming from a strong club such as Sydney,” McKay said.
“He’s a powerful right-footer with plenty of leg speed who makes good use of the football.
“Matthew only turned 20 on Monday, so his addition fits with our overall strategy to lower the age profile of our team.”
Dick worked with former Swans defender Marty Mattner, now an assistant coach at the club, during his time in the harbour city.