The 26-year-old has been recruited on an initial one-year contract and will compete with Peter Crook for the starting jersey, following George Willis' departure earlier in the month, and trained with the Pilgrims on their return to action on Saturday morning.
Fitzsimons has spent time with Crystal Palace and Bolton Wanderers, albeit without making a senior appearance, but made his name during three years at Meadow Lane.
United manager Craig Elliott was delighted to be able to sign such a prominent goalkeeper ahead of the new campaign, saying: "After losing George, it was important we signed another top class keeper and I am delighted we have managed to sign somebody so highly regarded as Ross.
"He's very hungry to be successful and I am looking forward to working with him this season.
"We now have two outstanding keepers in Ross and Pete, so it's an area we are really strong in."