The company, which won an exclusive agreement to develop the project in 2009, said it now plans to concentrate on its onshore business.
However, FOR said it would complete Ireland’s 1GW Coding Park offshore project in the Irish Sea, which received government consent in 2005.
FOR won the Forth Array project in 2009. It was among four offshore developments in Scottish waters totalling 2.7GW and is separate to the bigger Round 3 offshore tender.
In a statement, the company said: "FOR sees a clear future for offshore wind and believe it will make an important contribution to the recently announced Scottish government renewable targets as part of the UK commitment to 2020.
"Our decision to step back from the Forth Array project is a consequence of our intention to concentrate our investment in those projects we feel we can best deliver in the short to medium term. Plans will now include additional investment in our Scottish onshore development portfolio."
Last month’s move by Vattenfall to cancelled if plans add 51MW expansion to the 300MW Thanet offshore wind farm.