Job losses will be partially offset by hiring for the production of its CSeries commercial jets, it said.
It is cutting 580 jobs from its Belfast operation this year and potentially a further 500 next year.
Bombardier says it is Northern Ireland's largest manufacturing employer.
It has a Northern Ireland (NI) aerospace workforce of 6,000, and says it accounts for 10% of NI's manufacturing exports.
Around 200 Bombardier employee jobs in Northern Ireland are currently at risk of redundancy.
"We deeply regret the impact this will have on our workforce and their families, but it is crucial that we right-size our business in line with market realities," a spokeswoman said.
Davy Thompson of the Unite union told Radio 5 live: "There's been a drip-feed of job losses over the past 14 months, with probably about 800 job losses on the Belfast site, so it's not a major shock something has come along.
"Certainly over 1,000 would be a hammer blow for us in terms of Northern Ireland manufacturing."
Bombardier will also cut 270 management and contractor jobs at its trains business in the UK, with 44 permanent positions to go. The UK rail business employs 3,500 people.
The firm said it had made a net loss of $5.3bn (Â£3.7bn) in 2015, and had revenues of $18.2bn - 10% lower than the year before.
Bombardier also forecast lower revenues for 2016, saying it expects to generate between $16.5bn and $17.5bn.
The 7,000 posts to be cut will include 2,000 contractors, and will fall mainly on the transportation and aerostructure parts of the business.
The company said it had signed a letter of intent with Air Canada for up to 75 CS300 aircraft for as much as $3.8bn, based on the list price.
Bombardier has been helped by recent cash infusions from the Quebec pension fund, Caisse de Depot et Placement du Quebec, and the Quebec provincial government.
Canadian plane and train maker Bombardier will cut its workforce by about 7,000 over the next two years, it has said.