Sigurdsson returned to the Liberty Stadium - where he had previously enjoyed a loan spell - following a mixed two-year stint with Tottenham Hotspur.
The 23-year-old has had an immediate impact, scoring the winner in Swansea's shock 2-1 win over Manchester United on Saturday, and Williams envisages big things for the Iceland international this season.
"He can be massive for us this season," Williams told the South Wales Evening Post. "That's why the chairman paid so much money for him, because he has got that little bit of quality we need to go forward.
"He was a bit of squad player at Spurs, but he is going to be very important for us.
"He is a very clever player. He gives us that bit of quality with a set-piece or a finish that we might have missed and we're delighted to have him. He knows how much we like him here and hopefully he will have a big impact."
The former Hoffenheim ace enjoyed a solid first spell in South Wales, scoring seven goals in 17 Premier League appearances under Brendan Rodgers after joining in January 2012.