The move, confirmed as a straight loan with no option to buy, addresses one of Real Sociedad's most pressing needs after the summer departures of Aritz Elustondo and Duje Caleta-Car left head coach Pellegrino Matarazzo short of options at the back.
Sarr becomes the Basque club's first signing of the transfer window, arriving in San Sebastián after passing a medical and completing the paperwork between the two clubs.
The 20-year-old struggled for opportunities at Stamford Bridge, making only seven appearances since joining from Strasbourg for a reported fee in the region of €14m in June 2025, with regular football hard to come by under Liam Rosenior and Calum McFarlane before Xabi Alonso's arrival as head coach further reduced his prospects.
Despite the lack of club minutes, Sarr was still called up by Senegal for this year's World Cup, having helped his country to the Africa Cup of Nations title earlier in the year.
Speaking to reporters after completing the move, Sarr explained why he had chosen Real Sociedad.
"I decided because it's a great club in Spain. It's in a very good league and, since it's the second-best league in the world, I really wanted to come here — I thought it was a very good option for me," he said.
"Whether I can play as a left-sided centre-back, which is what the club was looking for? I've played on the right and on the left, I have no preference and no problem with either."
Sarr also revealed he had sought advice from Alonso before finalising his decision, though his mind was already made up.
"I already spoke with Xabi, but I'd already made my decision. He told me the city was very beautiful, that the people are lovely, that the fans are incredible and that I was going to enjoy it here in San Sebastián."
Regular football is what he is chasing above all else after a difficult stretch on the periphery in west London.
"I feel a lot of motivation. What I'm missing is playing — it's been a long time since I played with any continuity, and what I want is to be on the pitch and be able to help my team-mates," he said. "I don't feel pressure, I feel motivation to help the club as much as I can. Already Thursday? Yes, I'm ready."
Standing at 1.94m, Sarr came through Lyon's academy before spells at RWD Molenbeek and Strasbourg preceded his move to Chelsea. He is expected to link up with his new team-mates in training this week, with Real Sociedad still searching for the further defensive reinforcements Matarazzo has publicly requested.