The transaction, which also includes the Kinneil Terminal, will see Ineos take control of a system that delivers almost 40 per cent of the UK’s North Sea oil and gas.
The groups were first reported to be in talks over a potential sale last month.
The Forties pipeline was opened in 1975 by BP and today consists of more than 100 miles (161km) of pipes with the capacity to transport 575,000 barrels of oil a day from fields in the North Sea and several Norwegian fields.
Ineos chairman and founder Jim Ratcliffe said: “The North Sea continues to present new opportunities for Ineos.
“The Forties Pipeline System is a UK strategic asset and was originally designed to work together to feed the Grangemouth refinery and petrochemical facilities.
“We have a strong track record of acquiring non-core assets and improving their efficiency and reliability, securing long-term employment and investment.”
Under the terms of the deal, Ineos will pay BP £99.5 million ($125m) on completion and an earn-out arrangement over seven years that totals up to a further £99.5m ($125m).
BP chief executive Bob Dudley said: “While the Forties pipeline had great significance in BP’s history, our business here is now centred around our major offshore interests west of Shetland and in the Central North Sea.”
Forties employs around 300 BP staff at Kinneil, Falkirk, Dalmeny, Aberdeen and offshore.
Ineos is best known in Britain its shale gas fracking operations.