The versatile Pugh, who can to play in central midfield, left midfield or at left-back, will remain at Hillsborough until the end of the season.
The 30-year-old will be available for the Owls' npower Championship game at Charlton on Saturday.
Pugh has had two spells at Leeds along with Preston & Stoke, since coming through the youth system at Manchester United in 2002.