The former Scotland assistant recently confirmed he would not be renewing his contract when it ended in the summer.
However, a brief statement released by the Tannadice club said: "Peter, who recently confirmed he would not be renewing his contract at the club, led Dundee United to Scottish Cup success in 2010 and helped the squad qualify for European football on three consecutive occasions. He leaves with the thanks of everyone at the club and best wishes for the future."
United last night cancelled today's press conference ahead of the Clydesdale Bank Premier League clash with Motherwell at Fir Park tomorrow, with a spokesman claiming that there had been too much speculation in recent days.
It was reported this morning that United chairman Stephen Thompson met with Falkirk manager Steven Pressley and Partick boss Jackie McNamara last night as they stepped up their bid to replace Houston.
Dundee United face Rangers at Tannadice in the Scottish Cup on Saturday in a game which is the subject of an official boycott by the Ibrox club.
When announcing his decision to leave, Houston cited further cutbacks combined with his own desire to progress as a manager as the motivating factors.
He added: "I want to be part of a successful Dundee United but I have my concerns - and my concerns are the fact that we have to compete on the pitch.
"There is only so much you can do if you continue to cut.
"I'm the first to understand that the club has to cut, they can't afford to keep going on.
"The Thompson family isn't a bottomless pit. The chairman and directors have to look after the financial side.
"Me, as a football person, wants the best team on the pitch."