Republic of Ireland international Clark had been without a club since leaving the Magpies in the summer.
The 34-year-old joined United from Aston Villa in August 2016 and was the club's player of the year as they won the Championship title in his first campaign. He made 127 appearances for the Magpies in all competitions, scoring 11 times, and spent last season on loan with Sheffield United, helping them gain promotion to the top flight.
With two promotions from the Championship under his belt, Clark will now hope to achieve another with Stoke this term - although Alex Neil's men are currently just outside the relegation zone.
Clark, who has been reunited with former Magpies team-mate Dwight Gayle at the bet365 Stadium, told his new club's official website: "I've missed the feeling of being in the dressing room and preparing week-to-week for Saturdays.
"I worked hard throughout pre-season and have kept myself in good shape since, so I am keen to get out there with the lads over the next couple of weeks, as the feeling of those sessions is something you can't replicate alone.
"With the quality of players we have, if we find some consistency, I believe we can go on and have a good season."