Agreement on the deal was reached in August 2019 but remained conditional on clearance from the Competition & Markets Authority, which was received last week.
Jacobs has bought a business that designs, delivers and maintains strategic and complex nuclear assets, primarily for customers in the UK.
Wood's environment and infrastructure consultancy will continue to deliver environmental, regulatory and permitting support, including large-scale remediation of radiological constituents in various markets including North America.
Jacobs is a US firm with several UK legacy brands, including Babtie Shaw & Morton, Allott & Lomax, Sir Alexander Gibb & Partners and Halcrow.
Wood has been taking action to reduce its debt burden. It also recently sold its industrial services business.
Wood's chief financial officer, David Kemp, said: "Future portfolio optimisation will continue to be driven by our strategic objective of building a premium, differentiated, higher margin business focused on energy and built environment end markets. The sale of our nuclear business and other recent divestments have also enabled us to accelerate progress towards our leverage target."