Greenwood joins City fresh from winning the UEFA Women's Champions League with Lyon, much like compatriot Lucy Bronze who completed the same move hours before her.
The 27-year-old left-back crosses the Manchester divide having played for United two seasons ago.
She has also made the Merseyside switch, having previously played for both Liverpool and Everton.
"I think I've come back to England at a perfect time," Greenwood said to Sky Sports.
"The league's going from strength to strength. The players who are coming over speaks for itself and I'm really excited to be a part of it.
"For me it's about winning trophies. [Manchester City's] ambitions and my ambitions went hand in hand.
"I'm realistic, I know that we've got a few new faces, but this club's about winning and the history speaks for itself.
"Domestically they've won trophies every single season and I'm coming in to continue that, and hopefully that starts this season."
