The Scotland midfielder had one season to run on the four-year deal he signed on arrival from Liverpool in the summer of 2012.
He made it clear earlier this year he wanted an extension, and a deal has now been struck, according to Adam.
He tweeted: “Delighted to have signed a new contract with Stoke City.”
The news was not immediately confirmed by Stoke, and Adam gave no further details.
Back in March he said: “I love it here. Some people seem to think I’m going to go in the summer, but I’m not going anywhere.
“I’ve still got a year on my contract and I will see it out, and if the club wants to see me about a new contract then I will speak to them.
“I’ve been here nearly three years now and hopefully I can stay here for many more years yet.”