The clubs had previously announced an agreement over a fee for the 25-year-old defender, with United promising a further announcement on Twitter.
Greenwood celebrated her move on Twitter, writing: “So excited to be joining @OLfeminin the best women’s club in the world and to test myself against the best players everyday. Excited for the journey ahead.”
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Liverpool-born Greenwood played one season with United in the Women’s Championship, England’s second-division, joining the club in their debut season.
She scored four goals in 18 league games for the club, helping to guide them to the title and promotion to the Women’s Super League.
But her successful campain for United will be her only one, as she moves toFranceto suit up for Europe’s most dominant side.
Lyon have captured six of the last nineChampions Leaguecrowns, including four straight from 2015-16 through 2018-19.
The club have also dominated domestically, having captured the title every season in the French top flight dating back to 2007, a run of 13 straight seasons.
Greenwood joins a side that features reigning Ballon d’Or winner Ada Hegerberg and France stars Wendie Renard, Amandine Henry and Eugenie Le Sommer.
L’Olympique Lyonnais est heureux d’annoncer l’arrivée de l’Internationale anglaise@AlexGreenwoodau poste de latérale gauche en provenance de Manchester United.
Bienvenue Alex ! 🔴🔵pic.twitter.com/vfKFBGYb3f
— OL Féminin (@OLfeminin)August 8, 2019
The defender’s Lioness team-mates Lucy Bronze, Nikta Parris and Izzy Cristiansen also feature for Lyon.
Parris’ move fromManchester Cityto the European Champions was announced in June, as she joined on a three-year contract.
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Greenwood started four games for England at this past summer’s Women’s World Cup, scoring a goal as she helped the Lionesses to the semi-final, where they fell to the eventual winners, the United States.
Prior to her time with United, Greenwood featured atEverton, Notts County and Liverpool, all in the Women’s Super League.
Lyon get their 2019-20 season underway when they faceMarseilleat home August 24.