She takes over from previous housing minister Keith Brown who has moved to transport.
The addition of the welfare brief in the ministerial shake-up reflects the importance of housing in aiding economic recovery and also the challenges facing those in poverty.
Burgess will report to Nicola Sturgeon who moves from health secretary to infrastructure Investment and Cities as well as taking on the substantial brief of responsibility for the independence referendum.
She swaps posts with former housing minister Alex Neil.
First Minister Alex Salmond said: “This strong ministerial team will take this Government forward in meeting the economic and social challenges we face while creating a better Scotland for future generations.
“As Health Secretary, Nicola Sturgeon has demonstrated what can be achieved when Scotland has responsibility for its own affairs.
She has delivered record low waiting times and protected the NHS from the creeping privatisation of the UK Government.
“As cabinet secretary for Infrastructure, Investment and Cities, she will have a lead role in our programme for economic recovery.
With responsibility for Government strategy and the constitution, she will also lead in making the positive case for Scotland’s future.
Mike Leonard, Director of the Modern Masonry Alliance, said: “The Modern Masonry Alliance in Scotland looks forward to working with Margaret to promote more house building using locally sourced materials.
"We will be seeking an early meeting to discuss how building 50,000 additional public rented homes across Scotland will begin to address the growing housing crisis in Scotland whilst driving jobs and growth the country so badly needs.”
