Members of the Rail, Maritime and Transport union had been due to walk out on Friday and Saturday in a dispute over the role of guards and other issues.
Virgin had said it would have run a normal service if the strike had gone ahead.
In a message to RMT members, general secretary Mick Cash said the company had confirmed there will be a train manager on every passenger service, carrying out safety critical duties previously carried out by the guard, and it is not the firm’s intention to change this.
“Management has also reiterated that there will be no compulsory redundancies as a result of these changes,” he said.
David Horne, Virgin Trains’ managing director on the east coast route, said: “We’re pleased that the RMT has agreed to suspend industrial action and continue talks.
“We had put in place detailed contingency plans which would have seen our timetable run as normal, nevertheless this news will be welcomed by our customers and people.
“We’re making exciting changes on the east coast as part of the customer-centric revolution which has seen us embark on a £140 million investment programme in our trains and stations.
“The on-board changes have already resulted in an improved customer experience.”
Virgin said it had given assurances on each point raised by the union at the start of the dispute, including keeping the safety critical duties on-board.