The British monarch chatted with Ono, John Lennon's widow, while visiting the Museum of Liverpool in the northwest England port city where the Fab Four was formed.
Ono said she was impressed by the queen's burgundy coat, dress and matching hat, saying it "made her look so young, so elegant. She is always elegant. It's always nice to meet her."
To honor the queen's trip to Liverpool Thursday, the band of the Coldstream Guards played a medley of Beatles songs during the Changing of the Guard at Buckingham Palace in London.
The Associated Press contributed to this report.