Talks reached a successful conclusion on Friday with Gremio accepting Benfica’s offer but inserting a profit-based sell-on clause.
If Benfica sell Everton for more they are paying now, Gremio will receive 15% of any profit.
The media have different takes on the price, with €20m to €24m reported, but Benfica will pay in installments over three years.
Only a few documents need to be exchanged before the deal can be formally announced.
24-year-old Everton will fly to Lisbon over the weekend for a medical before signing his contract.
It will be Everton’s first experience in Europe after becoming one of the Brazilian league’s biggest stars.
In total, Everton has scored 69 goals in 274 matches for Gremio and has appeared 14 times for Brazil.
Everton arrives at Benfica at the request of returning head coach Jorge Jesus, who made a personal phone call to the player.