The Canadian international, who celebrates his 32nd birthday today, signs a contract until the end of the season, subject to international clearance.
Dunfield is no stranger to the region, playing for Manchester City, Bury and Macclesfield earlier in his career.
The midfielder, who left FC Toronto in October, has been on trial with the club and the manager is happy to get a deal sorted.
He said: "With the immediate loss of Anton Rodgers to injury, I didn't feel we could take any chances. Terry has good pedigree and has impressed us while on trial."