Cleaver's move comes after the £42m takeover of the group by Balfour Beatty at the end of last year.
Sources close to Cleaver at the time said he would resign "in a matter of months", enough time for him to help with the integration of Mansell into Balfour Beatty.
Mike Peasland, who is currently managing director of specialist subcontractor Balfour Kilpatrick, will replace Cleaver on 5 April. There will be a four-week handover period.
The job of working as the managing director of an unlisted company is totally different. I didn’t want to go backwards
Cleaver told Building: "I'm in discussions with a number of people about non-executive positions. There is also the option of working for private equity businesses advising on investments."
Cleaver said that he wanted to leave because his role had been changed by the takeover. He said: "The job of working as the managing director of an unlisted company is totally different from working as the managing director of an operating company. I didn't want to go backwards."
Balfour Beatty said that very little would change under Peasland's leadership. It said: "The reason we bought Mansell was that it was a perfectly complementary business that does not compete with our existing businesses."
In January, its first full month's trading since Balfour bought the firm, Mansell had the highest monthly order intake in its history.
A Carillion insider said Houson had been headhunted as he had "a wealth of experience" managing PFI schemes.