Cobham, a world-leading expert in air-to-air refuelling, said new US owners Advent International would maintain a UK headquarters, continue funding research and development at its Dorset offices and keep using the Cobham name.
Contracts with the Ministry of Defence (MoD) and the Home Office will also continue to remain in the UK, with a "commitment not to restructure the UK operating companies' capacity in a way that would result in some, or all, of the relevant activities being developed and/or supplied from outside the UK without the written approval of the relevant (Government) department".
Any future sales of parts of the business must be passed by the MoD and Home Office too, it added.
The deal, which was first approved by shareholders in August before going to a review by the Competition and Markets Authority and Government departments, is now expected to be concluded on January 17.
Shonnel Malani, partner at Advent, said: "Advent takes its custodianship of Cobham seriously, and we are confident the transaction and undertakings being given on national security, jobs and future investment, provide important long-term assurances for both Cobham's employees and customers, particularly in the UK and also globally."
The Government's decision to allow the deal to pass without a more in-depth investigation has already been criticised by the family of Cobham's founder.
Late on Friday, Business Secretary Andrea Leadsom gave the deal the go-ahead after Advent agreed to the legal undertakings outlined on Monday.
But Lady Nadine Cobham, the daughter-in-law of the company's founder Sir Alan Cobham, said: "This is a deeply disappointing announcement and one cynically timed to avoid scrutiny on the weekend before Christmas.
"In one of its first major economic decisions, the Government is not taking back control so much as handing it away.
"In Cobham we stand to lose yet another great British defence manufacturer to foreign ownership, through a takeover that would never have been approved by the Americans, French or Japanese, all of whom have taken steps recently to raise protections for their own defence sectors."
Prime Minister Boris Johnson defended the sale over the weekend.
He said: "I think it's very important that we should have an open and dynamic market economy.
"A lot of checks have been gone through to make sure that in that particular case all the security issues that might be raised can be satisfied and the UK will continue to be a very, very creative and dynamic contributor to that section of industry and all others."
The business was founded in 1934 as Flight Refuelling Ltd, before listing on the stock market in 1985.
The firm's air-to-air refuelling systems played a key part in the 1982 Falklands war.