The group's North American operation is expected to start work at the space centre in Florida next March, although final details of the deal are still being thrashed out.
The contract is set to span at least five years, with a base contract worth $159 million and a further possible $1.8bn.
Qinetiq's work will include designing and developing ground systems and equipment for ground processing of Nasa launch vehicles and spacecraft, as well as technology for the space agency's mission requirements.
The deal is a welcome boost for the UK firm, which employs some 6,000 workers in the UK, as it faces a major spending clampdown by the Ministry of Defence, while it is also vulnerable to defence cuts in the US where it has significant operations.
The group has staff in nearly every North American state and its clients include Homeland Security Agencies and the US department of energy. The US division was formed through a string of acquisitions, starting with American firms Westar and Foster-Miller in 2004.
Qinetiq's US team already works for Nasa at the Glenn Research Centre in Ohio and the Goddard Spaceflight centre in Maryland on aerospace engineering, IT and testing.
Nasa has itself been a victim of cost cutting following the global recession, with President Barack Obama recently slashing the manned space programme.
Its $108bn Constellation programme to get astronauts to the Moon by 2020 and Mars by 2030 were cancelled, although the president committed to help Nasa continue with vital research work with a view to future deep space missions.