The company plans to use the money to focus on its core business. Bombardier's military aviation training business consists of 200 employees supporting NATO training in Canada.
Bombardier is the world's only maker of both plains and trains and is headquartered in Montreal and posted revenues last year of $18.2bn.
Marc Parent, CAE's President and chief executive officer, said:
We are happy to welcome Bombardier’s Military Aviation Training team to CAE. We are also proud to now operate one of the world’s premier military pilot training programs and deliver the total training required, including support for live aircraft training, to produce the military’s next-generation fighter pilots.
We plan to expand the NFTC program, and leverage our new capabilities into future integrated training systems programs worldwide
The company has had a bumpy month after it cut its financial outlook and suspended the development of the Learjet 85 programme. The move will cost the Canadian firm approximately $1.4bn (£923m) in the fourth quarter of 2014.
Bombardier said its cash flow for 2014 would amount to $800m rather than the previous forecast of between $1.2bn and $1.6bn.