Lawyer David Sherborne explained to the High Court that the lyrics had been changed before the release of the Rudebox album in 2006, and he said that Robbie Williams "wishes now to apologise publicly".
David Sherborne also said: "Robbie Williams did not intend to allege that Nigel Martin-Smith has ever stolen any funds from Take That or anyone."
Gary Lux, who was representing Nigel Martin-Smith, said after the hearing that the former Take That manager had never wanted the matter "to come this far".
Nigel Martin-Smith was in charge of Take That from their start in 1990 right through to their end in 1996.
Robbie Williams had already left Take That in 1995 to begin a solo career in pop music.
