The board of Newcastle-based Wellstream, which has twice rebuffed the US conglomerate, finally gave its support after GE upped its takeover price from 750p a share to 780p, valuing the company at about 785m.
GE will also pay a special dividend to Wellstream shareholders, worth 6m.
Wellstream, which makes pipeline products and systems, has two manufacturing facilities, at Newcastle and in Brazil, and employs more than 850 staff. Petrobras, the Brazilian oil firm, is one of its biggest clients.
The deal beefs up GE's presence in the UK, which includes Aberdeen-based oil services company Vetco Gray.
Subject to shareholder approval, the business will operate as part of GE's oil and gas subsidiary, which designs and makes surface and subsea drilling and production systems.
The deal is thought to be GE's biggest deal in Britain since it bought medical equipment maker Amersham in 2003.