Mowlem launched the claim, initially for £80m, because of an alleged breach of contract by the MoD after the project at its Abbey Wood headquarters in the city ran into difficulties. The dispute centred on the extent of Mowlem's liability for the delay.
The dispute went to arbitration last July, a month after an MoD offer to settle Mowlem's claim for £20m had been rejected.
Mowlem, however, decided to accept the MoD's offer after an interim decision by the arbitrator this summer.
The 130,000 m2 Abbey Wood complex, which houses nearly 5000 ministry officials, was opened by the Queen in 1996. It received praise for environmentally praiseworthy attributes but was four months late and criticised by parliament's public accounts committee.
Gains said that prospects for the group remained good despite the uncertain economic background.