The 21-year-old has been on the fringes of the first team this term but has largely been restricted to matches for the Under-23s, banking three goals and four assists in 15 Premier League 2 appearances.
Clarke has only played one game for the senior Spurs team this season - coming off the bench for the second half of their Europa Conference League Qualifying defeat to Pacos de Ferreira - and he will now spend the next few months in League One.
Speaking to safc.com, Clarke said: "I can't wait to get started. I'm from this part of the world, so I know this is a massive club and what it means to the fans.
"I'm looking forward to playing at the Stadium of Light and the prospect of being part of the team that takes the club back to the Championship. I want to help the team as much as possible, whether that's goals or assists, and ensure we reach that end goal."
Manager Lee Johnson added: "Jack is a talented player and having followed his progress over the past few years, I feel like he's really grown on the pitch throughout the past six months and found a maturity to pair with that talent.
"The competition for places in our final third is strong and we want to be able to change games as we move into the back end of the season. Jack understands that this is a big club with a lot to play for, but he wants to be an influential player for us and help to ensure we have a successful end to the season."
Clarke has made four appearances for the Tottenham first team in all competitions since arriving from Leeds United in 2019 and follows Trai Hume, Danny Batth and Patrick Roberts to the Stadium of Light this month. body check tags ::