The former Netherlands boss, who has been out of the game since parting company with Ajax in 2009, will assume control of the club in the summer
Jans had already stated that he would stand down when his contract with the club expires in the summer.
However, the appointment of Van Basten has come as a surprise as FC Zwolle boss Art Langeler had been considered the favourite to land the job, while the name of former Netherlands coach Louis van Gaal had also been mentioned in connection with the vacancy.
It is Van Basten, though, who will reportedly fill the void, having signed a two-year contract with the club.
The former AC Milan striker has been out of the game since parting company with Ajax in 2009 and is looking forward to resuming his coaching career.
"I have not much to report," the 47-year-old Dutchman told reporters on Monday. "I'm glad to be here and to have signed the contract.
"We spoke a few weeks ago, it went well and gave me a lot of confidence. So, I'm very pleased.
"Heerenveen is a nice club. I understand that the budget is not as great as in Amsterdam but I think that next season we can have a good squad."
However, Van Basten did acknowledge that there is a chance that the club could lose some of their best players in the summer.
"Scared is not the right word," he mused. "I rather think that we as a club should be proud.
"Like any club in this league, you're always forced to sell good players and then have new players to train."
Van Basten, who scored 24 goals in 58 games for Netherlands, was on the verge of rejoining the Amsterdam outfit in an executive role last year but talks over his proposed return eventually broke down.
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