The 24-year-old Ajax captain Klaassen, a product of their famed academy, scored 49 goals in 163 games for the club.
He also helped the Dutch side to reach this year's Europa League final where they lost to Manchester United.
Attacking midfielder Klaassen was persuaded to join Everton by their renowned Dutch coach Ronald Koeman.
“He’s an honest guy, we talked about the club, about the way he wants to play and that gave me a positive feeling," Klaassen told Everton TV.
"It’s difficult to leave Ajax but I think this is a good step for me now and I’m really looking forward to my time here.”
Klaassen has 14 caps after making his Netherlands debut in a friendly against France in 2014, scoring four goals.
“He’s a player who is only 24 but has a lot of experience and is a leader on the pitch," said Koeman.
"He has already captained Ajax for two seasons and that shows you the type of person he is.
“He is hardworking, likes to press and, of course, will give us more creativity and goals."
Pickford, who got his first call-up to England's senior squad in October, was one of the best players in a Sunderland side that finished bottom in the top flight last season.
Speaking about his move to Merseyside, the 23-year-old told the team website. "It's a great club, a massive club and I think it’s a great opportunity and the right time for me to come to Everton and show what I can do."
Pickford, whose fee which could rise to 30 million pounds based on team and individual performances, is in Poland with the England under-21s and the move to Everton will not be completed until July 1 when the international transfer window opens.
Everton finished seventh in the Premier League last term and qualified for the Europa League third qualifying round.
(Reporting by Ken Ferris in London and Hardik Vyas in Bengaluru; Editing by Mark Heinrich and Andrew Both)
Share
