The 31-year-old Scot revealed the news on his official Twitter feed, writing: "Delighted to announce that I have extended my contract with Stoke for a further year."
Former Rangers trainee Adam joined the Potters from Liverpool in August 2012 and has gone on to make 151 appearances.
While Adam has yet to play in the Premier League this season, the midfielder was in the team for the midweek 4-0 Carabao Cup win over Rochdale.