The 34-year-old will step into the breach for the struggling Stags after Kevin Pilkington was ruled out for several weeks with a lung injury.
Stags boss Keith Curle was reticent about plunging teenage keeper Jason White into the thick of a relegation battle and plumped for the experience of Welch.
"It has been a job trying to find the right player to fill Kevin's shoes at short notice but we think that we have found the right man," Curle told the club's official website.
"It is no reflection on Jason White that I have not picked him for the role. He is still well thought of but at the moment I feel that we need experience in goal."
Welch is a free agent after being released by Torquay United in December and has initially signed on a match-by-match basis.
Meanwhile, Mansfield have sent French forward Mickael Antoine-Curier back to Nottingham Forest after a trial at Field Mill.
Curle was impressed by the youngster but with Forest unwilling to sell and the Stags chief not prepared to use his last loan berth on Antoine-Curier, a deal has been put on the back-burner.
