It was co-written by Paul Simon (of Simon and Garfunkel) and Bruce Woodley (of The Seekers). According to Cyrkle guitarist Tom Dawes, Simon offered it to The Cyrkle when they were opening for Simon and Garfunkel on tour. The song's tracks were recorded in stereo, with the bass, lead guitar, and percussion on the right track, acoustic guitar and electric organ on left, and the vocals on both.
The Seekers also recorded "Red Rubber Ball" for their 1966 album Come the Day (US-title: "Georgy Girl") — and the Seekers' recording of "Red Rubber Ball" can also be heard on 'Disc Three - 1966 - 1967' of the CDbox setThe Seekers Complete.
At "Music Notes", the sheet music for "Red Rubber Ball", for the albumSimon and Garfunkel - Old Friends, also credits the songwriters as Paul Simon and Bruce Woodley