His departure comes just days after Ajax threw away the Eredivisie title on the final day of the season as a 1-1 draw with De Graafschap saw rivals PSV Eindhoven snatch the trophy.
Everton sacked Martinez on Thursday after a horrendous run of form culminated with a harrowing 3-0 defeat to Sunderland.
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"I had a fantastic time here. First as a player and the past decade as a trainer," De Boer said in a statement on the club's website.
Ajax then gave me the chance in the first team and I'm grateful to the club.
De Boer, who had been with Ajax since 2010, has regularly been linked with a move to the Premier League.
He has resisted those advances until now, but his agent’s recent comments that his client “would love to join a club like Everton” has sparked a frenzy surrounding the Goodison Park hotseat.
"After winning four league title in succession the 2014-15 season was a disappointment, that we wanted to rectify last season," De Boer added. "We have done everything but it has not become what we all hoped and expected.
"I began to realise more that it was time for me for something else. That is better for me and I think also for Ajax. What I will do, I do not know yet. A year without a club is also an option, I'll see what comes my way.
Ajax is my club and always will be.

Everton fans with a banner regarding Everton manager Roberto Martinez

Image credit: Reuters


'He would love to join a club like Everton or Valencia,' agent Guido Albers told NOS.
'It's all about the right philosophy and how they play football. That is what Frank is looking for.
'I have told Ajax there is no other club and I have not held discussions with anyone.'


The timing makes this very interesting. De Boer might be saying all the right things – “a year without a club is also an option” – but it’s unlikely you would resign this hastily from a five-and-a-half year stint at your favourite club unless something has caught your eye.
And if he lands the Everton job, he can’t really fail. The squad needs a defensive overhaul, but it should have still challenged for a European spot this season. They are 12th and 16 points adrift of seventh-placed Southampton.
The Toffees have been flaky this season. The early part of the campaign saw them dominate sides and still drop points; the latter part has seen them crumble after conceding. Perhaps De Boer’s winning mentality (this season’s final day meltdown aside) could rub off on an immensely talented but aimless group of players.
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