The Scottish international received the main award as he was named Player Of the Year, as voted for by supporters, and the Players' Player of the Year Award, in which he was the unanimous choice of his colleagues.
The 35-year-old stopper is the Whites only ever-present this season and he received his awards at a dinner at the club's Conference and Exhibition Centre.
Kevin Blackwell said: "Sully took a big wage cut to come here from Chelsea last summer. He wanted to join us and play, rather than sitting on Chelsea's bench and taking home a lot more money.
"He has shown remarkable concentration and consistency and has pulled off saves that have made a big difference. For me, he has been a tremendous signing and I hope he has another cracking season next time.
"Having said that, I think all our players deserve a gong for what they have achieved in very difficult circumstances this season."
Aaron Lennon was voted for by supporters as the Young player of the Year, just edging out Simon Walton for the award.
David Healy picked up the Goal of The Season award for his great effort against Plymouth Argyle at Elland Road on December 28.
Lucas Radebe was presented with the Best Contribution to the Community award and the Lifetime Achievement award.