London-listed Amec employs 29,000 people in around 40 countries and generates annual revenues of £4.2bn from markets including energy, mining and infrastructure.
Foster Wheeler has more than 13,000 staff in more than 30 countries. Both companies have bases in Aberdeen and Glasgow while Amec also has an office in Edinburgh.
Amec said it has provisionally agreed the terms of a cash and shares deal and the combination would create a new company valued at £5bn.
The two firms already work together after recently securing consultancy contracts in Kuwait for the building of a new refinery.