Mr Hague is to leave Parliament at the 2015 general election after 26 years as MP for Richmond, North Yorkshire.
As part of a significant ministerial reshuffle, veteran Conservative MP Ken Clarke has also stepped down.
Senior ministers have told the BBC that the current defence secretary, Philip Hammond, will replace Mr Hague.
Labour described the reshuffle as "the massacre of the moderates".
Mr Clarke, who first became an MP in 1970, attended cabinet as minister without portfolio.
He held a number of top cabinet positions under Margaret Thatcher and John Major, including home secretary and chancellor of the exchequer, and tried and failed three times to become Conservative leader.
In 1997, he lost out to Mr Hague, who went on to lead the party until 2001.
In other moves, David Jones has been sacked as Welsh Secretary, having been in the cabinet post for two years.
Prime Minister David Cameron said: "William Hague has been one of the leading lights of the Conservative Party for a generation, leading the party and serving in two cabinets.
"Not only has he been a first class foreign secretary - he has also been a close confidante, a wise counsellor and a great friend.
"He will remain as First Secretary of State and my de facto political deputy in the run up to the election - and it is great to know that he will be a core part of the team working to ensure an outright Conservative victory."
