It was written specifically for George Harrison to sing at a time when he lacked the confidence to compose his own material. Years later, McCartney described it as a "formula song", and Lennon said, "I would never have sung it myself."
Structurally, it features hectic Bo Diddley rhythm and busy banjo style guitar playing in juxtaposition with Harrison's vocal. Its composers give it an unpredictable choice of chord (augmenting the B7th on "I'm happy just to dance with you") right at the crux of its title, jarring the chorus. The song is also unique in that it begins not with a verse or chorus but with the last four bars of the bridge.
Anne Murray included a cover of "I'm Happy Just to Dance with You" on her 1980 album Somebody's Waiting. Murray had had some success in previous years covering other Beatles songs such as "You Won't See Me" and "Day Tripper." Unlike the Beatles' original, Murray's version of "I'm Happy Just to Dance with You" is an adult-contemporary ballad.
Murray's version of the song was released as a single in mid-1980, reaching No. 64 on the Billboard Hot 100 and No. 23 on the Billboard country chart.