The pair never faced a criminal trial over the allegations after the Crown decided not to prosecute, but Clair sued for damages and was awarded £100,000 last week as a judge upheld her version of events.
Goodwillie was dropped by Plymouth in the wake of the ruling but decided to ask for his contract to be terminated so that he could appeal the verdict.
"Plymouth Argyle Football Club Limited ('PAFC') confirm that David Goodwillie has left the club by mutual agreement," a statement said.
"Mr Goodwillie has asked the club to terminate his contract of employment in order that he can focus his time on a potential appeal of the civil judgement made against him.
"PAFC has agreed to his request. PAFC will make no further comment on this matter."
Robertson, meanwhile, has announced his retirement from football following the verdict.