The company has four locations in Larne, Belfast, Springvale and Monkstown.
FG Wilson, which is part of the international Caterpillar group, said the losses are part of measures to make the business more efficient and competitive.
The 760 job losses include about 170 agency workers who were informed in June that their jobs would go.
Union leaders said they were shocked by the scale of the redundancies.
The announcement was made as Northern Ireland First Minister Peter Robinson and Deputy First Minister Martin McGuinness headed a mini-summit to discuss the economy and Northern Ireland’s unemployment rate of 8.2%.
Robert Kennedy, the company’s Northern Ireland operations director, said: “We understand these decisions will be difficult for the lives of many of our workers and their families, and we genuinely regret that.
“We are striving to reduce some of the impact by offering an enhanced VR package.
“We’ll also help redeploy displaced workers by providing training on new skill sets, partnering with potential Northern Ireland employers to host job fairs and hiring a placement service.”
The company announced in June that it was moving production of its 400 series generator sets to Tianjin, China, in order to build the product closer to its growing customer base.
Mr Kennedy added: “We realise the announcements we’re making affect a company that has a rich history in Northern Ireland.
“However, given our current structure and economic environment, portions of our portfolio are not competitive, and we need to react accordingly for long-term growth and to compete for industry leadership.
“Caterpillar is committed to building the remaining business in Northern Ireland and to working closely with local government, including Invest Northern Ireland, as we’re focused on keeping it competitive and sustainable for the future.”
Unite regional secretary Jimmy Kelly said he was furious.
He said: “The high-calibre job losses are a crushing blow to the East Antrim area and Northern Ireland.
“The company has not given its workers or their union representatives the opportunity to negotiate a plan which would have attempted to keep some of the affected workers employed.”