Shaqiri, 29, has signed a three-year contract at the Ligue 1 side, ending his three-year stint at Anfield.
Liverpool released a statement on the official club website which read: "Everybody at Liverpool FC thanks Xherdan for his contributions over the past three seasons and wishes him the very best for the rest of his career."
The Switzerland international moved to Merseyside from Stoke City in the summer of 2018 and made 63 appearances for Liverpool, scoring eight goals in the process.
The forward's last goal for the club came in their 7-2 win over Lincoln City in the Carabao Cup last season.
Shaqiri captained his national team at Euro 2020 and guided them to the quarterfinal stage of the competition.
He will join a Lyon side looking to improve on their fourth-placed finish in Ligue 1 last season after they missed out on Champions League qualification on the final day.