Members of the Rail, Maritime and Transport (RMT) union will walk out on April 28 and 29 in a dispute over staffing and the role of conductors.
The union’s members on Norther Rail will also strike on April 28 - the third wave of action to hit the company.
Virgin said its “detailed contingency plans” meant a normal timetable would run, despite the industrial action.
The company has made changes to customer-facing roles on board, which see a single person on each train take responsibility for the “customer experience”, a move the operator says has no impact on safety.
“We have repeatedly assured the RMT that the safety critical role of the guard will remain on board, with the new train manager role taking responsibility,” said a statement.
RMT members on Northern Rail will strike for 24 hours next Friday. The company will operate a reduced service but will says it will “do our best to keep you on the move”.
Northern’s strike timetable is expected to be published shortly, but Sir Gary Verity, chief executive of the tourism body Welcome To Yorkshire, which is behind the three-day cycling event, said the industrial action was unlikely to have an impact.
He said: “The companies I have spoken to say there will be a full service.”
David Horne, managing director for Virgin Trains on the east coast, said: customers could “plan and book their journeys as normal and with confidence”.
He added: “The Bank Holiday weekend sees a number of exciting events on our route including the Tour de Yorkshire, so we wanted to do everything we possibly could to ensure we offer a full timetable and continue to support communities.” Virgin said it had given the RMT a guarantee of no compulsory redundancies .