The 23-year-old had been training with Jackie McNamara's side in recent weeks and has impressed enough to convince the Firhill boss to sign him up.
McGuigan is an Honours student at the University of Abertay in Dundee and a deal has now been sealed in time to beat the March 31 deadline in place for clubs in the SFL.
Jags boss Jackie McNamara said: "Mark was with Celtic as a youngster but left to study for an Honours degree in Physical Activity and Health at Abertay University, a degree that he is just about to finish.
"While studying, Mark has been playing Junior and amateur football and first came to our attention when we played a bounce game against the Scottish Universities team.
"Mark scored twice in that game and gave our defence a hard time. On the strength of that we invited him in to spend a few weeks training with us and he has continued to impress us.
"I'm looking forward to seeing him in action for the first team and he will go into the squad for tomorrow's game with Livingston.
Meanwhile, the Jags have finalised a deal to bring midfielder Sean Welsh back to the club until the end of the season.
Welsh's loan deal from Hibernian was due to expire today, but Thistle moved to bring the 22-year-old back to Firhill for the rest of the SFL campaign.