The Tannadice club had been holding discussions with Houston over a new contract as recently as Tuesday.
And Houston had also held talks with English Championship club Blackpool at the start of the week over the vacancy at Bloomfield Road.
Houston was appointed caretaker manager in December 2009 after Craig Levein left to take the Scotland job, and he was given a three-year contract following United's Scottish Cup triumph to following May.
United chairman Stephen Thompson praised Houston for his efforts but admits the current financial climate played a part in the decision.
Thompson said: "In an ideal world, we would have had no hesitation in renewing contracts on a similar basis as originally provided.
"However, the world has changed in the last three years and we must re-align the cost base of the business to the new economic reality.
"Peter fully understood this, but felt that with the direction the club has to go in, he could no longer continue to take the club forward.
"He will remain fully committed to his role as manager until the end of the season and will then leave with our best wishes and grateful thanks."