The 25-year-old winger's temporary stay at Elland Road had been set to end after Saturday's game against Leicester.
He has played five times for Leeds but, despite the loan extension, he has not been given permission to play against Sunderland on Boxing Day.
"I would be delighted to stay here for as long as manager Kevin Blackwell wants me," Oster told Leeds' official website.
"And Sunderland are happy to let me stay."