Sporting signed Vinagre, a product of their youth system, from Wolverhampton Wanderers on a permanent deal this month after a one-year loan. The 23-year-old made 18 appearances for Sporting in all competitions last season.
"It's a dream come true to join a big club like Everton," Vinagre said.
"The opportunity to work with very good players and a very good coach in Frank Lampard made me excited to sign."
Vinagre joined Wolves from Ligue 1 side AS Monaco in 2017 first on loan and then permanently a year later.
He then had loan spells at Greek side Olympiacos and Portuguese outfit Famalicao before making his return to Sporting.
Everton begin their Premier League campaign at home to Chelsea on August 6 after avoiding relegation by finishing 16th last season.
