Mansell originally planned to float in the late 1990s, but this was dropped after its failure to merge with housing group Lovell in 1998.
Anstee, who will join Mansell on 7 April, forms part of a new management team at the group. This includes chief executive Philip Cleaver and finance director Pat Scannell, formerly at housebuilder Bryant.
Cleaver said Anstee's City experience, which also includes a stint as chief executive the finance division of insurer Old Mutual, would be invaluable for Mansell.
He said: "He has a great reputation for doing deals. He is extremely well known in the City."
Cleaver said he had given himself two to three years to execute the plans for the group. He said: "We are exploring a variety of options right now. We do not anticipate doing anything in the next six months."
He added that the target was to create value for Mansell investors by looking for new investment: "Whether that comes from private individuals or from the City remains to be seen."
Cleaver said the firm was well ahead with repositioning itself on the market, changing from a traditional contractor to a property finance firm.
He said: "We are now much more a property services group. The key word is sustainability. We want sustainable relationships with clients so we get long-term cash-flow and more long-term value out of the business."
The group has £1bn of forward work from long-term relationships with clients such as BT, mobile phone company Orange and housing group Places for People (see page 16).
Anstee said this week that he was impressed with Mansell's work in property refurbishment and maintenance. He said: "I am impressed by the management team and believe that adding my own skills can ensure Mansell continues to flourish for the benefit of all stakeholders."