Coca-Cola - which has a global workforce of about 130,000 - said the cuts would be across all parts of its business and would impact about 500 staff at its Atlanta headquarters.
"At this time we have identified 1,600-1,800 positions in Corporate, Coca-Cola North America and Coca-Cola International that will be eliminated in the coming months," said the firm in an emailed statement.
"As part of our recently announced, multi-year productivity initiatives, we are redesigning our operating model to streamline and simplify our structure and accelerate the growth of our global business. As we have acknowledged previously, this redesign work will result in impacts to jobs across our global operations."
General Mills, meanwhile, said the Pillsbury plants in New Albany, Indiana (which employs around 400 people), and Midland, Ontario (which employs around 100 people), would likely close "mid-calendar year 2016". Both facilities have been operated by General Mills since the 1950s and manufacture refrigerated baked goods. The Indiana decision is subject to negotiation with union officials.
The move comes as part of General Mills’ $40m cost-saving program announced in June 2014 to kick-start improved efficiency and growth, and follows its November 2014 announcement to close its breakfast cereal production plant in Lodi, California – a move impacting 430 employees.