The Iceland international will undergo a medical on Wednesday to finally complete his protracted transfer to Goodison Park, according to reports.
WATCH: Gylfi Sigurdsson set for Everton switch after Swansea reportedly agree £45m sale
Everton have agreed a deal worth up to £45 million (Dh213m) for Swansea City playmaker Gylfi Sigurdsson.
The Iceland international will undergo a medical on Wednesday to finally complete his protracted transfer to Goodison Park, Press Association Sport reported.
The saga has dragged on for most of the summer with Swansea initially valuing Sigurdsson at £50m.
But Everton are finally set to secure their No 1 summer target at a price slightly lower than Swansea had wanted.
Sigurdsson, 27, pulled out of Swansea's pre-season tour to the United States after Everton's interest had become clear.
He rejoined first-team training upon Swansea's return from the States but he did not figure in their Premier League opener at Southampton on Saturday.
Swansea rejected two Everton bids for Sigurdsson, but Everton manager Ronald Koeman said last weekend that the deal was "still close" after reports that talks between the two clubs had broken down.
And Swansea manager Paul Clement was just as keen to close the deal to allow him time to find replacements before the transfer window closes at the end of August.
"The objective and the aim is that at some point the two clubs will meet," Clement said ahead of the goalless draw at Southampton.
"I think the way it's going there needs to be more than likely a compromise on both sides. That is very often how a deal is made.
"We are at a critical stage of this situation and hope it's going to be resolved very quickly."
Sigurdsson's importance to Swansea was underlined by the fact he scored nine league goals and had 13 assists as the club just avoided relegation from the Premier League last season.
Only two other players, Manchester City's Kevin de Bruyne and Tottenham Hotspur's Christian Eriksen, brought more goals and assists to their teams and Everton quickly targeted Sigurdsson as a key signing during a transfer window in which they have spent heavily.
Everton's majority shareholder Farhad Moshiri has spent close to £100m so far in recruiting former favourite Wayne Rooney, Jordan Pickford, Davy Klaassen, Michael Keane, Cuco Martina and Sandro Ramirez.
But that figure will now significantly rise with the capture of Sigurdsson, who can fill a variety of forward positions.
Swansea hope to use the Sigurdsson cash by strengthening their squad with two or three players before the window closes.
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Wilfried Bony, their former striker who appears surplus to requirements at Manchester City, and West Bromwich Albion forward Nacer Chadli are both on Swansea's radar.
And Swansea have also made an enquiry for their former midfielder Joe Allen, although Stoke City insist the Wales international is not for sale.
Swansea striker Fernando Llorente, meanwhile, will miss Manchester United's Premier League visit on Saturday.
Llorente returned to training on Tuesday after fracturing his arm on a cycling holiday but will not be considered for the United game.
"Because of the nature of the injury to the arm, he lost a lot of upper-body bulk," Clement said.
"We will take it day by day with him. Hopefully he will respond well to the training and will be available soon."