The appointment followed a tender process which initially involved nine agencies before a final four-way pitch shootout.
The aerospace company, which employs more than 3,000 people across 20 UK sites, is focusing on the expansion of its non-military offering.
Director of comms EMEA at Lockheed Martin, John Nielson, explained: "The consultancy work will focus on promoting Lockheed Martin’s reputation as a technology leader, a good employer and a good corporate citizen.
"Particular focus will be given to highlighting its contributions to the UK national economy, its move into adjacent markets such as IT systems to support transport, oil and gas and government organisations and its partnerships with research institutions and academia."
As well as working across the UK, Man Bites Dog will provide ad-hoc support for projects in other markets, Nielson added.
Last year Lockheed Martin acquired Scottish company Amor Group, which provides IT systems for the energy, public service and transport sectors.
Grayling, which had previously worked for Amor before transferring to work with Lockheed Martin, and Lockheed Martin's incumbent agency Hill+Knowlton Strategies are both understood to have been involved in the tender process.
Lockheed Martin will continue to work with Grayling until the summer.