The pair were accused of raping Denise Clair at a flat in West Lothian in January 2011 when they were teammates at Dundee United.
The crown decided not to prosecute and the footballers never faced a criminal trial, but Clair waived her right to anonymity and decided to sue Goodwillie and Robertson for £500,000.
The duo insisted that the sex had been consensual, but in a session at the Court of Session in Edinburgh, judge Lord Armstrong upheld Clair's version of events that she was too drunk to consent.
"Having carefully examined and scrutinised the whole evidence in the case, I find the evidence of the pursuer (the woman) to be cogent, persuasive and compelling," he said.
"In the result, therefore, I find that in the early hours of Sunday 2 January 2011, at the flat in Greig Crescent, Armadale, both defenders (the footballers) took advantage of the pursuer when she was vulnerable through an excessive intake of alcohol and, because her cognitive functioning and decision-making processes were so impaired, was incapable of giving meaningful consent; and that they each raped her."
A spokesman for Plymouth told BBC Sport: "We note today's judgment from the Court of Session in Edinburgh regarding David Goodwillie. We await the full report, which we will consider in detail before making any comment. Until such time, David Goodwillie will not be selected to play for Plymouth Argyle."
Cowdenbeath have yet to respond to the ruling.