The pair both shared tributes to the legendary musician, who died in New York in 1980, after he was shot by Mark David Chapman.
Sharing a black and white photograph of them together on Instagram, Sir Paul wrote: “I love this picture, it reminds me of the bond between us. Happy 80th John. Love Paul”.
Overnight, Beatles drummer Sir Ringo Starr also remembered John.
He posted on Instagram: “Let’s celebrate John‘s 80th birthday with come together Friday, 9 October I still miss you man peace and love to Yoko Sean and Julian.”
Yoko Ono, John’s wife, also posted a short video showing New York’s Empire State Building lit up in blue, and with a peace sign, in honour of his birthday.
“Happy birthday John! It’s lit!” she wrote.
In his hometown of Liverpool, the council has launched a worldwide contest to find another great songwriter in honour of his birthday.
A collection of previously unseen pictures of Lennon in New York will also go on display at The Beatles Story in Liverpool.
A pop-up TV channel called LENNON80 has also launched, which will feature special programming, including the documentary charting John and Yoko’s Bed-In For Peace in Montreal, Canada, in 1969, as well as the couple’s 1971 interview on Parkinson.