The toll-free bridge – which was one of 29 major “transport priorities” outlined by the Government today – will be constructed for between just £1.72 and £2.34 billion.
Original plans for the bridge could have cost more than £4 billion.
But under the new proposal the existing Forth Bridge will be made a dedicated public transport-only corridor, meaning the new crossing can be built much narrower.
The announcement was made in the Strategic Transport Projects Review, which sets out the future investment programme for transport in Scotland over the next 20 years and is the biggest and most ambitious Scottish transport plan ever published.
In a statement to Parliament, transport minister Stewart Stevenson also signalled progress on other fast-tracked STPR projects including the Edinburgh-Glasgow Rail Improvement Programme, the Highland Main Line and rail services between Aberdeen and Inverness.
Mr Stevenson said: "Good transport infrastructure is vital to delivering increased sustainable economic growth.
"The plans I have set out today clearly identify where we as a government see the priorities for investment against a backdrop of increasing pressure on our budget. This is a significant programme of prioritised schemes for delivery and the whole of Scotland is set to benefit.
"The Scottish Futures Trust will be central to securing maximum value for money for the public purse. As a centre of expertise which facilitates project collaboration, it will help release up to £150 million a year in extra investment in the fabric of Scotland's public services."
He added: "To ensure effective delivery, we will take forward an action programme with key delivery bodies in the New Year."
Other key projects under the plan include upgrades to the A96, including dualling between Inverness and Nairn and a package of improvements to the A90 between Aberdeen and communities in the north east.