"All this happened so quickly because only a few weeks ago I was captaining Sunderland in their pre-season friendlies, but manager Steve Bruce made it clear that he was going to bring in new faces and he couldn't guarantee me a place."
The signing of Collins takes Stoke's spending to about £18.5m during the summer transfer window.
Collins began his football league career at Chester City and moved to Sunderland for £140,000 in October 2004.
"Danny has been Sunderland's player of the year for the past two seasons, which speaks volumes for the impact he had at this level," said Stoke manager Tony Pulis.
"He can play at left-back or centre-back, which gives us further options along the back four."
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