De Boer's contract runs out next year but after their final day implosion in the Dutch title race Ajax announced they had agreed to part ways after their tour of china is completed.
Ajax went into Sunday’s final round of matches level on points with defending champions PSV Eindhoven but with a superior goal difference.
With their opponents, De Graafschap, sitting second from bottom, Ajax were favourites to deliver a fifth title under De Boer but could manage no better than a 1-1 draw, allowing PSV to finish two points clear at the top of the table.
"He told the management in a meeting he wanted to stop and agreement has been reached over the cessation of his contract," the club said in a statement on their website(www.ajax.nl).
De Boer is interested in possible jobs at Everton, who have won only one of their last 10 Premier League matches under Spaniard Martinez, or Valencia, his agent Guido Albers told Dutch television at the weekend.
De Boer took over from Martin Jol as Ajax coach in December 2010, winning his first match at the San Siro against AC Milan in the Champions League, and going on to a record four successive titles from 2011 to 2014.
"I had a fantastic time here, first as a player and for the last 10 years as a coach," said De Boer who won 112 caps for the Netherlands before becoming a junior coach at the Ajax.
"Ajax fast tracked me to their first team and for that I am thankful. After we won four successive titles, the 2014-15 season was a disappointment.
"We wanted to put that right this season and did everything we could. But unfortunately it did not turn out as we had hoped and I have begun to realise it is time for something else. That will be better for me and, in my opinion, for Ajax too," he said.
(Reporting By Mark Gleeson; Editing by Amlan Chakraborty)
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