The 35-year-old, who signed for the Potters in 2007, has been an integral part of the side that has solidified their presence in England's top division since 2008.
"If I was being brutally honest, I wouldn't have thought five years ago that I'd still be playing at this level, but I've dug in," he said.
"When I came to the club, the gaffer [Tony Pulis] said this is where he wanted to be and asked who wanted to be with him, and he and the chairman have kept their promises.
"We've got quite a few of the lads still here that were part of that."
Delap is expected to feature for Stoke when they entertain Maccabi Tel-Aviv in the Europa League on Thursday.