The song was originally composed by LennonMcCartney. The lead singer on the original was by Paul McCartney. Here is the information below from Wikipedia:
"The master take was recorded on 31 January 1969 as part of the 'Apple studio performance' for the project Get Back. Paul played the piano (a Blthner Flgel from Leipzig/former East Germany), John played the bass, Billy Preston played the organ and George Harrison and Ringo Starr assumed their conventional roles. Paul's lead vocal was backed by John and George (as seen in the film Let It Be). The master take included a quieter guitar solo by George (which can also be seen in Let It Be