Houston, who had been linked with the vacant managerial post at Blackpool, said recently that he would be leaving Tannadice at the end of the season.
However, both parties decided on Monday to bring forward his departure.
A brief statement released by the 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."
The Arabs currently sit seventh in the Scottish Premier League, having won just two of their 12 home games, with both of those victories coming in the opening month of the season.
Houston's last game in charge was Saturday's 1-1 draw at home to Ross County.
Dundee United chairman Stephen Thompson reportedly met with Falkirk manager Steven Pressley and Partick Thistle boss Jackie McNamara on Sunday night, with ex-St Johnstone and Bristol City manager Derek McInnes also linked with the post.
Thompson said: "You'll find out in the next couple of days where we are. I would prefer someone in place before this weekend."
Youth Director Stevie Campbell and assistant manager Paul Hegarty will take charge for Tuesday's trip to Motherwell.
Thompson added: "We've been working on it for the last wee while, quietly behind the scenes. We've had a very long list and we've taken our time.
"We've actually had time to look at what we would like and what we are looking for, which we have been doing for the last 10 or 12 days to be honest. Now it's time for us to move on from there."