The two companies, which have a combined market value of approximately £5bn, said the all-stock deal values Amec Foster Wheeler at £5.64 per share.
Amec Foster Wheeler shareholders will receive 0.75 of new Wood Group share for each share held and will own around 44% of the share capital of the combined group.
The combined business should see cost savings of £110 million, Wood Group said.
Wood Group chairman Ian Marchant said the deal was a "transformational transaction" for the company, and that the merger will create a global leader across a range of industrial sectors.
"The combination extends the scale and scope of our services, deepens our existing customer relationships, facilitates further development of our technology-enabled solutions and broadens our end market, geographic and customer exposure," he said.
John Connolly, chairman of Amec Foster Wheeler said: "Combination with Wood Group adds to the standalone prospects of Amec Foster Wheeler, by accelerating the delivery of the future value inherent in the Amec Foster Wheeler business and, at the same time, helps to realise the full potential of each of Amec Foster Wheeler and Wood Group. The all-share structure of the offer allows our shareholders to benefit from the significant synergies and other strategic benefits that are expected to be realised from the combination."
M&A expert Jonathan Beastall of Pinsent Masons, the law firm behind Out-Law.com said: "Public M&A is clearly on the horizon for many companies with this deal coming hot on the heels of the merger between Standard Life and Aberdeen Asset Management and the announcement of approaches for Bovis Homes and is a great testament to the confidence and strategic vision of the boards of 'GB plc'."
"Given the impending triggering of Article 50 to commence Brexit, talk of a second referendum in Scotland and forthcoming politically sensitive elections in Europe along with the potential collapse of the London Stock Exchange merger it is hugely encouraging to see that companies and investors are prepared to sanction very significant deals in the UK market," Beastall said.
"While all-share mergers do not swell the cash holdings of institutions, M&A activity has an important trickle-down effect on the IPO market as listed shares provide a very potent acquisition currency for those companies wishing to join the markets and expand. Buoyant and vibrant M&A and IPO markets bode well for London’s reputation as the financial capital of Europe in the post-Brexit world," he said.