Greenwood had been suspended since January 2022 by the Premier League side over the allegations but prosecutors dropped charges including attempted rape and sexual assault in February.
"Getafe have reached a deal with Manchester United for the arrival of Mason Greenwood on loan for a season," said the Madrid side in a statement.
Last week United and Greenwood mutually agreed the striker would leave Old Trafford.
"The move enables Greenwood to begin to rebuild his career away from Manchester United," said the Red Devils in a statement.
"The club will continue to offer its support to Mason and his family during this period of transition."
Greenwood's signing comes during a sexism storm in Spanish football, surrounding the suspended president of the Spanish football federation (RFEF), Luis Rubiales.
The 46-year-old chief was provisionally suspended by FIFA for 90 days after forcibly kissing Women's World Cup star Jenny Hermoso on the lips on August 20 after Spain won the tournament in Sydney.
Getafe president Angel Torres said Rubiales could not stay "a minute more" in his post.
English prosecutors said they were dropping the charges against Greenwood after key witnesses withdrew and new evidence came to light.
Greenwood, whose contract runs until June 2025, said last week: "I did not do the things I was accused of, and in February I was cleared of all charges.
"However, I fully accept I made mistakes in my relationship, and I take my share of responsibility for the situations which led to the social media post."
He added: "The best decision for us all, is for me to continue my football career away from Old Trafford, where my presence will not be a distraction for the club.
"I thank the club for their support since I joined aged seven. There will always be a part of me which is United."
Greenwood was tipped for stardom at United after rising through the Old Trafford youth system and went on to score 35 goals in 129 senior appearances for the club.