The London-listed firm confirmed it has entered into a definitive agreement where it will make a cash and shares offer for the Swiss construction and engineering company
Both businesses are big players in the UK oil and gas sector, with bases in Aberdeen and Glasgow, while Amec also has an additional office in Edinburgh.
At the moment, Amec's oil and gas arm is focused on the offshore upstream market, while Foster Wheeler is more geared towards the onshore and downstream markets.
While the deal still has regulatory hurdles and shareholder approvals to clear, analysts from Canaccord Genuity suggested yesterday's announcement "significantly reduces the risk" of it not going ahead.
Samir Brikho, Amec chief executive, said: "The combination positions us across the whole oil and gas value chain, provides scale in our growth regions and is expected to be double-digit earnings-enhancing in the first twelve months."
The transaction is expected to fully complete in the second half of this year.
Alongside that, Amec also announced flat pre-tax profits of £255 million for 2013.
Total revenue fell 3% in the year, from almost £4.1bn to £3.97bn.
Amec said its European revenue grew 14% to almost £1.3bn, which was mainly driven by oil and gas activity in the North Sea.
It highlighted a number of contract wins, including a two-year renewal for BP's Forties Pipeline System, modification to the Tern production platform for Taqa and engineering, procurement and construction work across the UK North Sea for Nexen. Amec also worked on a consultancy basis with Zero Waste Scotland during the year.
The European order book grew 10% to £1.7bn, which Amec said reflected its "continued strong position in oil and gas".
It signalled a positive outlook for operations in Europe across 2014 and predicted revenue growth alongside an improvement in margins.
Mr Brikho said: "Strong performances from our oil and gas businesses in [the] UK North Sea and the Middle East and from US renewables offset weaker markets elsewhere.
"We continue to expect good underlying revenue growth in 2014, with ongoing strength in the conventional oil & gas and clean energy markets."
Amec further said it had renewed a major gas contract in the southern North Sea, which analysts suggested was worth around £100m of annual revenue.
Amec shares closed down 12p, or 1.1%, at 1080p.