The 54-year-old confirmed in a joint press conference with chairman Stephen Thompson that he will leave Tannadice when his current contract expires this summer.
Houston had been in talks over a new deal but has opted not to remain at the Clydesdale Bank Premier League outfit on reduced terms.
The Tangerines boss is determined to end his United career on a high by ensuring the club finishes in the top six again this term.
He said: "I'm going to stay until the summer and a lot of people will question that in terms of my motivation.
"My motivation is much higher to finish in the top six again than it's ever been.
"I hope the supporters stay with us because there is nothing I would like more than to finish in the top six and have another fantastic run.
"I'm very highly motivated. If I have four years in the top six, it's an even more impressive CV.
"The fans might think I'm going to down tools for the next few months but they don't know me as a person if they think that."