When making the Anthology miniseries, Yoko provided some home tapes of John playing piano and singing some unreleased songs he was working on. One of them was Free as a Bird, which was mostly incomplete. After massive tweaking and cleaning of the tapes, Paul wrote a new verse or two to fill in the gaps, and Paul, George, and Ringo "finished" the song basically by putting music to John's vocals. This resulted in the song released in 1995 as "Free as a Bird," which is credited to all four Beatles.
There were two other songs the band was considering using, but one was considered unusable due to the condition of the tape, and the other was an early version of "Real Love," which Lennon had finished at one point and recorded but not officially released until long after his death. This version contained almost completely different lyrics. Unlike Free as a Bird, Real Love was complete lyrically, so all the lyrics are John's. Once again, after extensive cleanup, the remaining three "finished" it, and the result was "Real Love," released in 1996. Both songs are also included on the Anthology CDs, "Bird" the first track on Anthology 1 and "Love" the first track on Anthology 2.
So technically, they are John Lennon solo songs that the surviving members of the Beatles finished almost twenty years later, and 15 years after his death. Also, if you do consider them part of the Beatles' discography, Real Love was the last song the Beatles released, not Free as a Bird.