The Glasgow full-back received over 24.6 % of the public vote - that's 29,734 fans.
CJ Stander came in second place with 14.9% of the vote. Third place was awarded to Louis Picamoles with 12.8% of the votes, followed by Joe Launchbury (8.9% of the vote). Finn Russell finished 5th (8.3 % of the vote), ahead of Conor Murray in 6th with 7.9 % of the vote.
Stuart said: "To receive this award again is an absolute honour, particularly when you take other players on the shortlist into account. I'm delighted to be awarded the RBS Player of the Championship Trophy and would like to take this opportunity to thank everyone who voted and the fans for their continued support throughout the Championship."