The post is Mr Bowman's first chairmanship, which he holds alongside his role as chief executive of engineering company Smiths Group.
Blackstone's GSO division led a £160 million equity injection into Miller Group in return for a 54% stake in March.
Mr Bowman said: "I am delighted to join The Miller Group at a very exciting point in its development.
"Its financial strength has been transformed by the recent capital injection by GSO Capital Partners and The Blackstone Group.
"The Miller Group has a very successful track record of producing many fine buildings and developments and the outlook for the future is extremely positive."
Mr Bowman, who was born in Australia, has spent much of his corporate life at the helm of Scottish companies and has overseen several multi-billion-pound sales.
He was chief executive of ScottishPower when it was sold to Spanish utility giant Iberdrola in 2006 for £11.6 billion. He had joined the company earlier that year on a contract that had an unusually lengthy two-year notice period.
Previously, he headed drinks giant Allied Domecq when it was swallowed by France's Pernod Ricard in 2005 in a £7.4bn deal. He had joined the owner of Ballantine's whisky as finance director in 1998 before being made chief executive a year later.
Also in 2005, as chairman of the bookmaker Coral, he oversaw the group's sale to fellow private-equity-backed gambling company Gala. He previously spent 10 years with pubs group Bass and had a brief stint in his native Australia in 1995 as finance director of retailer Coles Myer.
Mr Bowman was appointed a non-executive director of Edinburgh-based drinks company Scottish & Newcastle in 2006. It agreed to be taken over by Heineken & Carlsberg in 2008.
After taking the top job at Smiths in late 2007, Mr Bowman had been expected to break up the company, which has a sprawling set of industrial interests, most of them in the United States.
But this appears to have been put on hold by the financial crisis and the impact of state spending cuts, and Mr Bowman has since led a cost-cutting drive.
A Miller Group spokesman declined to comment on whether Mr Bowman's appointment is a signal that Blackstone is keen on a rapid sale or break-up of Miller Group.
Blackstone has previously indicated that it regarded Miller Group as a vehicle for consolidating troubled construction companies. The private equity house led a financial restructuring, which also saw Royal Bank of Scotland take a 23% stake, after Miller entered the housing crash with debt of around £1bn.
In 2011, Miller recorded a pre-tax loss of £92.8m after taking £62.4m of writedowns. This was an improvement on the £158.8m deficit of the previous year.
Miller Group chief executive Keith Miller said: "Philip has had a wealth of experience at the helm of major international public companies. He has amply demonstrated his ability to take a leading role in building businesses.
"We are looking forward to welcoming Philip to the Miller team at a time when we will be focusing on the further development and expansion of the business."