The 27-year-old, who has won the women's World Cup and Olympic gold with her country, will join the French club on loan from NWSL side Orlando Pride.
Morgan said the decision to leave "wasn't easy" but she hoped the move "pushes my game to another level".
She said she plans on returning to Orlando in June but Lyon say there is an option for another year in the deal.
Lyon won the treble of Champions League, French league and French cup last season, and club president Jean-Michel Aulas said Morgan's signing proved their desire to "invest at the highest level".
The NWSL season runs from April to September, while the French season is from September to May.
Morgan, who has scored 73 goals in 120 games for the US, was in 2015 the best-paid player in women's football, with her estimated earnings reaching £1.9m with endorsements. In the same year, she appeared alongside Barcelona forward Lionel Messi on the cover of the Fifa 16 video game in North America.
"I'm in my prime right now, but my prime isn't going to last forever," she wrote in a blog post at The Players' Tribune.
She added: "I'm not looking to coast. Just going through the motions isn't something I'll ever be comfortable with. I want to be the best player in the United States, the best player in the world so I've decided to take a huge risk and bet on myself.
"After a few weeks of deliberation, I finally made this decision during a belated honeymoon that I recently took with my husband, Servando, in Europe.
"I will be leaving Servando and my family - and our dog, Blue - behind, and I know from years of experience that phone calls and FaceTime are not a fun way to stay connected.
"I know, too, that the Pride and our incredible fans will be opening a state-of-the-art new stadium without me, and that I will miss the early part of the season. All of those things made it very difficult for me to make this decision.
"But my motivation is pretty simple. I hope that training with these incredible athletes each day, and learning a unique style of play, is exactly what I need, and that it will help me find that next gear."
United States striker Alex Morgan will move to reigning European champions Lyon for six months from January.