"Richard did a fantastic job for this club and I am delighted that things have worked out well for him at Bramall Lane," said Stoke manager Tony Pulis.
Cresswell has scored three goals in nine appearances for United and is aiming to help Kevin Blackwell's men return to the Premier League.
"This club is geared to the Premier League," the former Sheffield Wednesday frontman told United's official website.
"I am sure we can mount a strong challenge for promotion in the second half of the season.
"We are still in contention despite all the injuries we had before Christmas, but they have all cleared up now and we are ready to push on."
He added: "I will never forget the wonderful time I had at Stoke and I was delighted to play a key role in helping them to get where they are today."
Watford 6/4, Sheff. Utd 7/4, Draw 12/5