Starr (real name Richard Starkey) replaced the musician in 1962 when the group was managed by Brian Epstein in a decision which caused controversy.
Best, 78, tweeted: "Thought about it and thought why not. Happy Birthday Ringo. It’s a special one. Have a good day.”
Thought about it and thought why not. Happy Birthday Ringo. It’s a special one. Have a good day. https://t.co/xx854mv1mm— Pete Best (@BeatlesPeteBest) July 7, 2020
Best had originally been invited to go along with the group in 1960 to a series of club dates in Hamburg, Germany.
Epstein fired him from the Beatles in 1962 at the behest of members John Lennon, Paul McCartney and George Harrison, paving the way for Starr to step in.
After spending time in other groups, Best went to work as a civil servant for 20 years. He returned to the music industry in 1988 with the Pete Best Band.
The release of Beatles compilation album Anthology 1 in 1995 saw Best receive a substantial sum in royalties due to the use of tracks with him featured on drums.
Upon reaching the milestone birthday, Starr also received well wishes from a number of famous faces, including his fellow surviving Beatle, Paul McCartney.
Posting a photo of Starr to Instagram, McCartney wrote: "Happy birthday SIR RICHARD alias RINGO. Have a great day my long time buddy!”
Meanwhile, Lennon's widow Yoko Ono shared to Twitter: "Happy, Happy Birthday Ringo! Lots of peace and love, Yoko."
Elton John also wished the drummer a happy birthday from himself and husband David Furnish.
Posting a throwback photo of the pair of them to Instagram, John commented: "Happy 80th Birthday Ringo!! One of the world’s kindest people. And an inspiration to us both."
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