The Iceland midfielder, 27, scored nine goals and assisted 13 to help save the Swans from Premier League relegation.
Sigurdsson's fine form has prompted speculation linking him with a move to clubs such as Everton.
"It's a good honour for me. It's always nice when you get voted for by the fans and the players," he said.
"It's been a very good season for me personally with goals and assists and a good ending for the team."
Centre-back Alfie Mawson, 23, was named Swansea's young player of the year having joined from Barnsley in 2016.
There were also awards for top-scorer Fernando Llorente and Oliver McBurnie, who is under-23s player of the year.
But it was Sigurdsson who dominated Wednesday's awards ceremony at the Liberty Stadium.
After playing a starring role in Iceland's improbable run to the Euro 2016 quarter-finals, Sigurdsson signed a new four-year contract with Swansea in August.
He has continued to impress this season and, despite the Swans languishing towards the bottom of the Premier League table for much of the campaign, Sigurdsson has provided more assists than any other player in the division.
As a result, the former Tottenham playmaker continues to be linked with a move away from the Liberty Stadium, though Swansea head coach Paul Clement has said keeping Sigurdsson will be one of his priorities this summer.

The photographer, who has visited India more than 60 times, once said the country had taught him to watch and wait on life.
"If you wait, people would forget your camera and the soul world drifts into view," he told an interviewer.
McCurry, whose picture of a young orphaned Afghan girl with green eyes became an iconic image of war and the most recognised picture in the history of National Geographic magazine, has now published a book of his pictures of India.
"These magnificent pictures, some justly famous, many new and revelatory - reveal the beauty of the country and highlights its extraordinary contradictions," writes author William Dalrymple in his introduction.
"This is a very different India indeed, and it is here, in the places suspended between modernity and tradition, that most of the pictures in the book were made."
Here is a selection from Steve McCurry: India published by Phaidon/Roli Books.
Gylfi Sigurdsson has been named Swansea City's players' and supporters' player of the year for the second successive season.
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Celebrated American photographer Steve McCurry has been coming to India for more than three decades.