The announcement was made by Transport Secretary Chris Grayling in the House of Commmons.
It is the third private operator to fail to complete its full term in running services on the route.
The franchise, which operates trains between Edinburgh, Aberdeen, Inverness, Glasgow and King's Cross, was operated by the UK Government from 2009 to 2015 after the last collapse.
It reported losses on the line and in November past year Mr Grayling announced that the franchise would be terminated in 2020 to enable it to become a public-private railway.
"The route has its challenges, but it is not a failing railway".
Services continue as normal, pre-booked tickets will remain valid, and staff will be transferred to LNER.
Former transport minister Lord Adonis labelled the government's decision a "bailout" for the companies that would cost the taxpayer billions of pounds.
The loss-making service is being renamed London and North Eastern Railway (LNER).
An "Operator of Last Resort" run by officials at the department will take temporary charge of services, he told MPs.
Virgin Trains East Coast's contract will terminate on June 24 2018.
Stagecoach Group will hand back operation of the East Coast Main Line to the government, the train operator has said.
"We are surprised and disappointed that the Department for Transport has chosen not to proceed with our proposals".
He added: "However, we respect the Government's decision".
The company's subsidiary, East Coast Mainline (trading as Virgin Trains East Coast), is the current operator of the InterCity East Coast rail franchise under an agreement with the department for transport.
Trains on the East Coast Mainline will gradually transfer to LNER branding from VTEC branding.
"Three times in under a decade, private companies have failed on the East Coast".
"Anything else risks playing out the same expensive farce over and over again".
"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".