"I've learned so much about myself over the past 15 months by living away from home and in a different culture and environment, but it's given me so much time to develop both personally and as a player," Greenwood said in a statement.
"Now is the time for a new challenge though and having experienced such a successful campaign last season, when you get that taste for a winning mentality, it's addictive and I just want to continue that with City."
"We're delighted to have added Alex to our already strong squad ahead of the new season," City head coach Gareth Taylor said.
"She is a proven England international who will fit right into the group we have here at City, while she has also been involved in a number of successes recently to add accolades to her already impressive career so far."
She captained United as they gained promotion to the Women's Super League in their debut season as a team.
The full-back has made 46 appearances and scored three goals for the Lionesses including one during England's 2019 World Cup win against Cameroon.