The two clubs had been discussing a deal for the playmaker worth 60m euros (£52.75m) - 55m (£48.35m) plus a maximum of 5m (£4.4m) add-ons.
"Olympique Lyonnais is delighted to be able to count on the presence of their captain in 2018-2019", Lyon said in a statement.
The uncertainty carried into Saturday - much to the annoyance of France boss Didier Deschamps, who wants all of his players to have solved their futures before travelling to Russian Federation for the World Cup - before Lyon pulled the plug at 7pm on Saturday night.
A product of Lyon's successful youth academy, the skillful forward has 58 goals in 161 games for Lyon. The Brazilian superstar moved to Barcelona for a fee of €120m, which, in turn, allowed Liverpool to splash the cash on Fekir this summer.
Anthem at EA Play 2018
Battlefield V will put players into the chaos of World War II, bringing the franchise full circle back to where it all started. Whether plunder, revenge, or glory lures you onward, your choices will irrevocably change you - and the world around you.
The France worldwide was expected to join Jurgen Klopp's side before Les Bleus left for the World Cup, but OL have now ended talks and called off the deal.
Speculation is swirling about why the deal has not been rubber-stamped.
A source told ESPN FC on Thursday that Liverpool were confident about securing a €60 million deal for the France global, despite earlier comments from Lyon president Jean-Michel Aulas that no transfer would be concluded before the World Cup.
Liverpool did not attempt, suggest or offer to renegotiate any terms for Fekir.
He continued: "We need three or four players in, but if we get that, I think we can genuinely challenge Manchester City".