The British monarch chatted with Ono, widow of John Lennon, on a visit to the Museum of Liverpool in the northwest England port city where the Fab Four 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."
In honor of the queen's trip to Liverpool on Thursday, the band of the Coldstream Guards played a medley of Beatles songs during the Changing of the Guard at Buckingham Palace in London.