The contract, at Great Minster House and two other departmental buildings nearby, will begin on 1 July.
The deal will last five and a half years, with a possible extension of another four and a half years.
Contractual responsibilities include: building engineering services; cleaning; waste disposal and pest control; catering; reception and conferencing requirements; security and mail porterage.
Mel Ewell, chief executive of Amey, said: вЂњThis prestigious contract win is a further validation of the appeal of AmeyвЂ™s fully integrated end-to-end service, which builds in efficiencies through both scale and strategy. We won the contract because of the high quality of our response and look forward to delivering a full facilities management service for this important client.вЂќ