News of the transfer broke on Friday evening, with Bayern confirming the transfer via their official Twitter account.
The Portuguese midfielder, who has won two Bundesliga titles in his three years at the Allianz Arena, is the latest arrival in what has been a busy summer at Lille, following the likes of Yusuf Yazici, Victor Osimhen and Timothy Weah through the door.
Bayern chairman Karl-Heinz Rummenigge said: "Renato Sanches asked us for the transfer because he wanted to join a club where he plays regularly.
"Unfortunately, we could not guarantee him this at Bayern. Match practice is also important for him because he wants to keep his place in the Portuguese national team for EURO 2020.
"I would like to thank Renato for his achievements and wish him all the best for his future on behalf of FC Bayern."
First team football has been hard to come by for the 22-year-old since he arrived at Bayern from Benfica in July 2016.
Despite becoming the first Portuguese player to win the Golden Boy award for best European player under the age of 21, he struggled for form in Germany and failed to register a single goal or assist in his first season.
His season-long loan at Swansea and foray into the Premier League did little to inspire confidence in a player who had reportedly struggled to settle into the German way of life and master the language.
The Swans were relegated to the Championship at the end of the 2017-18 season, while Sanches suffered an injury-plagued campaign that limited him to just 15 appearances in all competitions.
Since returning to Bayern in July last year, manager Niko Kovac gave the player further opportunities to live up to his sizeable price tag, but a regular place in the starting XI continued to evade him.
On the international front, Sanches was a European Championship winner with Portugal in 2016 and was named Young Player of the Tournament.