Houston had been in talks with the Tannadice side over a new deal but has decided against the offers on the table.
The news was announced at a joint press conference on Thursday with the Tangerines boss and chairman Stephen Thompson.
The 54-year-old was granted permission to speak to Blackpool recently but does not appear to be in the running for the vacancy at the Championship club.
Houston stepped up from his role as assistant to Craig Levein when he left to take over as Scotland manager in December 2009.
He led United to the Scottish Cup in May 2010 and will seek to secure his fourth consecutive top-six finish in the SPL before he leaves.
United released a statement as the media conference started thanking Houston for his services.
It read: "Peter has now advised that he has decided not to extend his contract, as it is in the best interests of both the club and himself to remove any further uncertainty regarding the position."
In the statement, chairman Stephen Thompson said: "We are all extremely grateful to Peter for all of his efforts over the last three years as manager and indeed in his previous role as assistant manager.
"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.
"We are certainly not the only Scottish football club, or Scottish company, taking such action to ensure the future of the business and all of its employees.
"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."
Houston added: "First, I would like to thank the fans, players, staff and the board for their unbelievable support during my time here.
"I am sure that I can count on that support until the end of my contract.
"It is with sadness that I have arrived at this decision but feel that I have worked with the board to help them financially to reduce the debts and ongoing costs over the last three years and that there is a limit to how much we can continue to cut costs and continue to deliver what I want on the pitch.
"I understand and accept that changing circumstances mean that the board is under continued pressure to reduce costs, but I feel the time is now right for me to move on for a fresh challenge.
"I look forward to working with everyone at the Club to ensure we finish top six again as we have done for the last three years."
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