The 25-year-old has only recently returned to first-team training following injury, and he has not been involved for the 20-time English champions during the 2022-23 campaign.
Tuanzebe's contract at Old Trafford is due to expire at the end of June, and he is widely expected to leave the Red Devils on a free transfer at the end of the season.
The defender will now have the chance to secure regular football in the final months of this campaign, though, as he has completed a loan switch to Stoke.
"Manchester United defender Axel Tuanzebe has completed a deadline-day loan move to Stoke City until the end of the season," read a statement on Man United's official website.
"The homegrown defender has battled a series of injuries in recent years and he has not featured under Erik ten Hag as a result.
"But he has been working hard on his fitness all campaign and is now looking forward to registering some minutes on loan."
Tuanzebe has made 37 first-team appearances for Man United since debuting in 2015, while he has also spent time out on loan with Aston Villa and Napoli over the last few seasons.
"It was important that we added to our defensive resources and Axel is a player who knows the Championship and is keen to test himself at this level again," Stoke boss Alex Neil told the club's official website when the deal was confirmed.
Meanwhile, Stoke technical director Ricky Martin said: "Axel's pedigree speaks for itself, and we are delighted he will be with us for the remainder of the season."
Tuanzebe became the Championship side's fifth signing of the January market, with Ki-Jana Hoever, Bersant Celina, Ben Pearson and Matija Sarkic also arriving on loan.
The Potters are currently 18th in the Championship table, but they have won three of their last four matches in all competitions, including a 4-0 victory in their last league game on January 21.
Tuanzebe could make his debut for his new side against Luton Town in the Championship on Saturday.
Man United, meanwhile, brought in three players during the January market, all on loan, with Marcel Sabitzer following Jack Butland and Wout Weghorst to Old Trafford.