The deal will see the Scotland-based IT firm become part of Lockheed Martin's information systems and global solutions business, the company said.
Amor Group operates in the energy, transport and public services sector. Its acquisition is said to put Lockheed Martin into Britain's top 10 companies for IT services.
Employing around 600 people at offices in the UK, Dubai and Texas, Amor last year reported revenues up 27% to £57.2 million and trading profit up 22% to £8.1 million.
Chief executive John Innes said: "We were at the stage in our life cycle where we were looking at refinancing to support our growth ambitions as well as allow our private equity partners to exit in line with their original investment plans.
"The opportunity to become a part of Lockheed Martin is fantastic, not least because of the remarkable synergies between our cultures and ambitions. They offer a strong platform for growth in terms of talent, clients, geographic footprint, offerings and investment."
Stephen Ball, Lockheed Martin's UK chief executive, said: "This transaction provides opportunities for both Amor Group and Lockheed Martin to grow through innovative IT technology and key international markets."
One of Amor Group's investors was Scottish Enterprise, the government agency promoting economic development and innovation.
Scotland's Finance Secretary John Swinney said: "Since the group was formed in 2009 Amor has seen significant growth and now employs over 600 people across the UK. That growth reflects both the skills and expertise of the company's management and workforce and Scotland's ability to nurture and grow highly successful technology businesses.
"This acquisition by one of the world's largest aerospace and technology companies demonstrates Amor's international standing, Scotland's attractiveness to global investors and their confidence in Scotland's economy. Through our enterprise agencies we look forward to continued working with the company and supporting further growth."
Headquartered in Maryland, Lockheed Martin specialises in global security and aerospace and employs around 116,000 people worldwide.