Paul McCartney wrote this about Linda Eastman, who later became his wife. It was the first song he wrote about her.
In the televised documentary The Beatles Anthology, Paul, George and Ringo are shown relaxing on a blanket outside. Ringo asks Paul what he wrote in India and Paul answers, "I Will." Then George begins playing this on his ukulele while he and Paul harmonize with it.
McCartney had the tune for a long time. While in India he made an unsuccessful attempt, together with psychedelic singer-songwriter Donovan, to pen a lyric to go with it, months before the final version