As part of a reapportioning of responsibilities, Griffiths who is an undersecretary of state, has become minister for small business and enterprise, with construction only part of his portfolio.
Speaking for the first time to Building, Griffiths said: "I am delighted to be construction minister – I have already been backing major UK companies in Mexico, Thailand, Japan, Vietnam and India. Construction is one of our most important sectors. I want the government and this great industry to continue to work together to deliver a world-class industry, producing a world-class product."
Brian Wilson, 54, resigned last week as construction minister after more than two years in the job to spend more time with his family.
During his reign, Wilson promoted the benefits of sustainable development as part of the government's energy review as well as publicly launching the anti-cowboy quality mark scheme.
As part of the reshuffle, building regulations minister Christopher Leslie was replaced by Phil Hope at the Office of the Deputy Prime Minister.
Leslie has been moved to the government's Constitutional Affairs Department.
Regeneration minister Tony McNulty has moved to the Department for Transport as undersecretary of state and transport minister John Spellar has moved to the Northern Ireland Office as minister of state. Nick Brown, the Department for Work and Pensions safety minister, is to be replaced by Des Browne, MP for Kilmarnock and Loudoun.
The demotion of the industry within the Whitehall pecking order was criticised by the Construction Products Association and the Civil Engineering Contractors Association.