Williams: Sigurdsson will be crucial for Swansea
Sigurdsson joined the Welsh outfit for a second time – permanently on this occasion – after crossing from Tottenham in a swap deal that saw Ben Davies and Michel Vorm head the other way.
The Iceland international scored the winner in Swansea's shock 2-1 win at Manchester United on Saturday and Williams believes it is just the start of things to come.
"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."
Swansea's surprise win sees them sitting fifth in the table but Williams is adamant no-one will be getting carried away.
Manager Garry Monk has seen a raft of experienced players depart the club in the close-season, with Michu – on a season-long loan to Napoli – Pablo Hernandez and Chico Flores all joining Davies and Vorm in leaving.
And while Swansea have brought in quality, in the form of Sigurdsson and Jefferson Montero, they are not expected to be among the pacesetters of this season's Premier League table.
"The coaches and the experienced players will make sure that no-one gets above themselves," Williams added.
"We all enjoyed the win at United, but we get back to work and focus on Burnley.
"If we don't win the next game, what we did at United means nothing."