The Red Devils signed the Brazil international Porto in October 2020, and he made 24 appearances for the club during the 2020-21 campaign before playing another 26 times in 2021-22.
Telles was not part of Man United manager Erik ten Hag's plans for the 2022-23 season, though, which led to him joining Spanish outfit Sevilla on loan.
The left-back featured on 38 occasions for Sevilla last term, including 27 in La Liga, and there had been suggestions that he could make the move to Estadio Ramon on a permanent basis.
However, Sevilla rejected the chance to bring in the 30-year-old on a long-term deal, with the club not believed to be prepared to meet Man United's asking price.
Telles was not included in the Red Devils squad for their pre-season tour of the United States, fuelling rumours that he would be leaving the club in the near future.
Al-Nassr have now secured his signature, with the Saudi Arabian outfit believed to have paid a fee in the region of €10m (£8.7m) to bring him to Riyadh.
"Alex Telles has completed a permanent move from Manchester United to Al-Nassr... we'd like to thank Alex for his contributions to the club over the last three years and would like to wish him all the best for the future," read a statement on Man United's official website.
Luke Shaw and Tyrell Malacia are set to be the two first-team left-backs at Man United again next season, with Alvaro Fernandez potentially leaving on loan and Brandon Williams on a permanent basis.
Telles has linked up with former Man United teammate Cristiano Ronaldo, who made the move to Al-Nassr earlier this year following his departure from Old Trafford.
Last season's Saudi Pro League runners-up, who have Luis Castro as their manager, have also brought in Seko Fofana and Marcelo Brozovic during the summer window.
Zidane Iqbal and Charlie Savage have left Man United this summer for FC Utrecht and Reading respectively, while David de Gea, Axel Tuanzebe and Phil Jones departed following the expiration of their deals.
The 20-time English champions have made two signings during the current window, meanwhile, bringing in Mason Mount and Andre Onana from Chelsea and Inter Milan respectively.
Ten Hag's side are now said to be focusing on a deal for Atalanta BC's Rasmus Hojlund, although it remains to be seen whether they can come to an agreement with the Italian side over a price.