Richards, 79, shared a video on Twitter of himself playing piano and sending well-wishes to Jagger.
"Happy Birthday, Mick. Long may we keep saying this to each other, Happy 80th! Love, Keith," he captioned the post.
Wood shared photos with Jagger from throughout the years, writing, "Happy 80th birthday @MickJagger!"
In addition, the Rolling Stones official Twitter account posted a compilation video featuring footage from Jagger's career.
"It's a special day today! Join us in wishing @mickjagger a very happy 80th birthday!! Keep on rockin' Mick!" the post reads.
Jagger thanked friends and fans for the well-wishes on Instagram, writing, "Thanks so much for all your lovely comments and birthday wishes!!"
Jagger co-founded the Rolling Stones in the early 1960s. The band completed its Sixty anniversary tour in August 2022.