Michael McCartney threatened legal action against the 59-year-old actor after realising his Just Four Guys piece was a colourful reinterpretation of the photographer's black and white shot of the Beatles, reported Contactmusic.
Brosnan painted the picture for his wife Cassandra Harris, who was a big Beatles fan, and had no idea it would cause a fuss.
Showing off the picture and the original McCartney photo during an appearance on Jimmy Kimmel Live, the movie star said, "Michael, bless him, took a little umbrage at it... because it's copyrighted and I didn't know anything about copyright... I just did the painting for her.
"Anyway, all is good. Michael's happy, I'm happy..."
Harris died in 1991 and Brosnan is now married to journalist-author Keely Shaye Smith.