SNP ministers had put the cost at £307m just three years ago to create the new Social Security Scotland agency and the bureaucracy associated with the devolution of sweeping new welfare powers.
Opposition parties have now raised fears over the future payment of benefits to vulnerable Scots.
Liberal Democrat leader Willie Rennie said: “There is a huge opportunity to build a system that tackles inequality and poverty, but that needs to be underpinned by a well-managed and well-run agency in charge.
“The SNP claimed they could set up an independent country in 18 months. Instead their new social security agency has been beset with delays and doubled in cost.”
The increase came to light in a new “business case” for the new benefits system.
“Current plans indicate spending on implementation will total £651m from 2018-19 to 2024-25,” the business case states.
“This one-off investment in implementation will benefit the people of Scotland and will be used by future governments for decades.”
The biggest single cost associated with implementation is £190m on the “chief digital office”, while £141m has been earmarked for “enabling capabilities”. In addition, £49m has been allocated to staff costs for testing and £38m for staff and systems development for low-income benefits and support for live running.
The business case adds that the UK-wide benefits delivered by the Department of Work and Pensions (DWP) benefit from systems built up over decades.
It adds: “We are constructing a brand new public service from the ground up.
“This includes building systems for financial payments, fraud, error and debt, document storage and delivery, case management, cyber security, telephony, redeterminations and appeals, and many others.”
Eleven benefits are being transferred from the DWP in the largest devolution of responsibility since Holyrood was established.
But SNP ministers came under fire last year when it emerged the devolution of many of the benefits had been delayed until 2024 after a pledge this would be delivered next year.
Social Security Scotland has already opened and has introduced seven benefits worth about £500m. But this rises to a massive £3.4 billion next year as Scotland takes over full responsibility for the complex disability assistance benefits.
Social Security Scotland will eventually deliver 16 benefits.
Conservative Adam Tomkins said: “Multiple benefits remain with the DWP years after devolution.
“And we now have an SNP government imposing yet more cuts on Scottish local government while its own budget goes up thanks to the consequences of UK spending.
“Having spent years criticising the UK government over welfare policy, the SNP is now finding out just how hard it is to deliver a fair and affordable benefits system.
“But if the Nationalists can’t even get the set-up costs remotely right, what chance do they have of administering payments properly?”
Mr Rennie also slammed the overruns, saying: “This money would be better spent in lifting up the more than one million people in Scotland living in poverty.”
The Scottish Government will introduce the Scottish Child Payment by the end of the year, while the new disability payments will begin with the Child Disability Payment this summer.
“We are building the new system from scratch – the most significant new public service to be created in Scotland since devolution,” Ms Somerville said. “By the end of this parliamentary term we will have introduced 11 benefits that will help over 800,000 people in the next year. And by 2024 we will deliver 16 benefits and reach 1.8 million children and adults, and pay out an estimated £4bn.
“We are creating a social security system with fairness, dignity and respect at its heart – a service that has been designed with the help of those that use it, to meet the needs of the people of Scotland now and in future.”