The 27-year-old Iceland international will cost the Toffees £45m plus add-ons, and is currently undergoing a medical on Merseyside ahead of completing the move this week.
The deal which could reach a maximum of £47.5m according to the Daily Mail, and creates a club transfer record for both Everton and Swansea. It brings the Toffees spending this summer to £125m although £75m was recouped on the sale of Romelu Lukaku to Manchester United.
It’s been the drawn-out saga of the summer with Swansea fending off all interest during the close season. However, the midfielder made it clear to Swans boss Paul Clement that he wanted to leave for a rejuvenated Everton.
Ronald Koeman created space for Sigurdsson in his squad with the sale of 36-year-old Gareth Barry to West Bromwich Albion on Tuesday.
Sigurdsson left the Swans once before, joining Tottenham from Hoffenheim in 2012 after a year-long loan spell at the Liberty Stadium. A return to the Valleys came in 2014 with Ben Davies going in the opposite direction.
Everton are keen for the Icelandic midfielder to bring his shooting boots with him. At White Hart Lane, Sigurdsson managed a goal every 6 games whereas he found the net every 3 games in the white of Swansea.