New Zealander Anscombe was appointed head coach in 2012 on a two-year deal to replace Brian McLaughlin. He led Ulster to the final of the RaboDirect PRO12 in his first season in charge, losing 24-18 to provincial rivals Leinster.
The news comes just weeks after Director of Rugby David Humphreys announced he was leaving to take up a role with Gloucester.
Ulster Rugby chief executive, Shane Logan, said:
"I would like to pay tribute to the contribution that Mark Anscombe made over the past two seasons and to thank him for his hard work and dedication.
"Everyone at Ulster Rugby wishes him well for the future.
"Les Kiss will have an expanded remit for the Province’s director of rugby and will lead the coaching staff, assisted by Jonny Bell and Neil Doak and will manage first team selection.
"His appointment allows us time to recruit for long-term success."
Les Kiss will start work at Ulster Rugby on July 19.
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