Noel Henderson, an Australian, will take over Gandy's role. He has been a Multiplex group director for 16 years.
The move comes as Multiplex plans to launch an expansion in the UK and across Europe.
A company insider said because of capacity issues in the UK construction market, there was room for Multiplex to expand.
He said: "The Multiplex group has beefed up its construction and development operations and will now look to acquire a contractor."
Multiplex was last month linked with a possible bid for Bovis, which is owned by its Australian rival Lend Lease.
Gandy is to become a board director with Multiplex UK's development arm. The insider said that he would be responsible for developing Multiplex's interests across Europe. He said the step was a sideways move for Gandy.
As part of the wider management reorganisation, Ashley Muldoon, project director for the Wembley National Stadium project in north-west London, will be promoted to the Multiplex UK construction board. He will be joined by Dan Ashby, Bob Coe, George Assimakopoulos and Simon Cook.
Andrew Scrivener, former head of projects at developer MEPC, has been appointed to the board of Multiplex's developments arm and Robert Newton has been made managing director of the facilities management division.
Multiplex group is due to report its first set of results to the Australian stock exchange in August following its decision to float last year.
n A contractor for a key part of the £5bn regeneration of the Millennium Dome site in Greenwich, south-east London, was due to be appointed as Building went to press.
The joint developers of the project are Lend Lease, Quintain Estates and Anschutz Entertainment. They signed commercial contracts with government agency English Partnerships and Greenwich council last Friday to press ahead with the regeneration scheme.
The 20-year scheme, masterplanned by Terry Farrell and Partners, will include 10,000 houses, 38% of which will be affordable, 340,000 m2 of office space, a hotel and 33,000 m2 of shops.