The bid, which values David Brown shares at 290p, comes just a week after the group admitted it was in talks with a potential bidder. The shares closed at 279.5p, up 36p.
Textron, which makes Bell helicopters and Cessna light aircraft, said it would integrate David Brown into its Fluid and Power division. Most of David Brown's 3,000 staff are likely to keep their jobs as the businesses barely overlap.
Chris Cook, the chairman of David Brown, said the company had agreed to the bid after deciding it was the best way to build up a global position in its markets. "As the world changes it is becoming increasingly important for our business to have global reach," he said. "But we had used up our capacity for debt and I can't use paper for acquisitions."
Like many smaller engineering stocks, David Brown's shares have been hit by the strong pound and concern about a global economic downturn. Floated at 170p in April 1993, the shares touched an all-time low of 162.5p last month.
Lewis Campbell, the president and chief executive of Textron, said the deal offered a "strong, global platform" and "new, key locations to Textron's global manufacturing presence".
Mr Cook said Textron was likely to continue developing the businesses. Textron is in the process of selling its financial division for $4bn (pounds 2.4bn) and is planning to invest the proceeds in its industrial operations.
Mr Cook and Chris Brown, the chief executive, have irrevocably accepted the bid on behalf of their joint 7.3 per cent holding. Henderson Investors and AMP Asset Management, which control 22.5 per cent, have also accepted the offer.