The pounds 86m cash element of the deal, which will also see Amey assume pounds 59m of Comax's debt, will be financed by a three-for-eight rights issue at 600p a share, raising pounds 67m.
The acquisition comes just months after Amey was trumped in its bid to to buy Servisair, the airline services company, and signals a permanent shift away from the group's traditional role as a construction company.
David Staples, Amey's chief executive, said the move was "a complete step change in Amey's development".
Comax was formed by a pounds 74m management buyout during the Ministry of Defence's privatisation of part of its Defence Research Agency (DERA) two years ago.
It relies on 12 MoD contracts for 75 per cent of its business and clients range from property management of the Police Authority Estate in Northern Ireland to the security of the MoD's website, which is subject to the most hacking attempts in the UK.
Mr Staples said he believed high-security support services is a fast- growing sector. "It's about knowing how to operate in a secure environment," he said.
An analyst said: "It's a superb deal. It's in keeping with Amey's strategy - they're now a support services company."
Amey shares closed unchanged at 722.5p yesterday.