The 37-year-old full-back accepted the chance to train with Leeds during their three-game tour of the Republic of Ireland following a seven-month break from professional football.
The former Scotland international is well known to Gary McAllister, after playing at Celtic for two seasons under his former Elland Road team-mate Gordon Strachan.
He was at Bournemouth last season, but after making 24 appearances he left, partly due to the club's financial situation.
Telfer also played at Coventry and Southampton before joining Celtic.