The 29-year-old has returned to Elland Road after a successful loan spell that saw him make 22 appearances between September and December.
Tonge scored five goals during his stay and United boss Neil Warnock was delighted to complete the signing of the experienced performer.
"Tongey showed what an important member of the squad he is," he said.
"I'm delighted we've been able to agree things with Stoke to bring him here permanently.
"I think people saw Michael get better as time went on and you could see what he brought to the side."