The news comes three months after Transport Secretary Chris Grayling told the Commons the big-money franchise would only be able to continue in its current form for a "very small number of months" as Stagecoach had "got its numbers wrong" and "overbid".
Stagecoach said it and Virgin had been negotiating for a new contract with the Department for Transport but that it understood Mr Grayling was "no longer considering" them for the deal.
It is the third time since 2007 that the 393-mile (632 km) route has been returned to government hands, highlighting the difficulties for private companies of accurately bidding to run services on the privatized train network.
Stagecoach reported losses on the line, and in November previous year Grayling announced that the franchise would be terminated in 2020 to enable it to become a public-private railway.
Labour described the decision to end the £3.3 billion contract as a "bailout".
There will be a short transition, so any passengers should carry on using Virgin Trains East Coast's customer and ticket booking services.
It reported losses on the line and in November previous year Mr Grayling announced that the franchise would be terminated in 2020 to enable it to become a public-private railway.
Stagecoach Group chief executive, Martin Griffiths, said: "We are surprised and disappointed that the department for transport has chosen not to proceed with our proposals".
Perth-based Stagecoach said: "We have now been advised by the Department for Transport that the Secretary of State for Transport plans to announce today that he intends to appoint the "operator of last resort" (OLR) to operate the InterCity East Coast trains services".
He added: "However, we respect the Government's decision".
The RMT, the largest rail union, called for the switch back to the public sector to be made permanent.
"In all circumstances ownership of the infrastructure will remain in the public sector, but the railway is at its strongest when it is a genuine partnership between public and private".
In February Grayling admitted the beleaguered East Coast mainline rail franchise had collapsed.