The ruling was made on Wednesday by Mr Justice Eady, sitting at the High Court in London.
The company must also pay costs, unofficially estimated at around £200,000, to Stransky, a former World Cup winner with South Africa.
"
I am now considering options for my future career
"
Joel Stransky
"We are flabbergasted by the decision - we will now consider our options," said club chairman Malcolm Pearce.
Stransky claimed damages after alleging Bristol Rugby had reneged on an oral contract agreed in a Bath restaurant on 10 April, 2000.
Bristol Rugby denied they had ever agreed terms with him, blaming former club director of rugby Bob Dwyer for misleading Stransky.
But Dwyer denied this, and the judge found in favour of Stransky, saying the club had "left (him) on a string for three months".
At the time of the alleged contract, Stransky was working for Leicester Tigers, but immediately began making plans to move to Bristol.
Bristol Rugby club chief executive Nick de Scossa had denied any contract had been agreed, but Judge Eady labelled his evidence "unconvincing".
Jonathan Crystal QC, for Bristol, has been given 28 days in which to lodge and appeal.
Stransky, previously fly-half and then coach with Leicester Tigers, was in South Africa and not present in court for the ruling.
He later released a statement thanking his legal team and adding that he was deciding what direction his career will now take.