The European Parliament has approved a bill which guarantees that Brits visiting the EU for short periods after Brexit will not need a visa, even if the country crashes out with no deal.
The three-month visa waier would be conditional on the UK granting the same rights to EU citizens in return.
It would apply whether or not Britain leaves the EU with a deal.
The bill was delayed over its description of Gibraltar as a "colony".
However the legislation was approved in Parliament on Thursday.
Its final draft includes the descripton of Gibraltar as a "colony of the British Crown".
The reference had been criticised by Labour's Claude Moraes, who called it "opportunistic" and "unnecessary".
This held up the bill, which had already been approved by the EU executive.
The new legislation would allow trips to the EU and four other countries for up to three months within any six-month period, the BBC reports.
However Brits will still need to pay €7 (£6.30) every three years to travel to EU countries after Brexit.
A British spokeswoman said in February that Gibraltar was a "full part of the UK family" and that it was "completely inappropriate" to call it a colony.
Gibraltarians, whose economy depends on an open border with Spain, voted overwhelmingly to remain in the EU in Britain's 2016 referendum.
Spain, which is holding national elections on April 28, sees Brexit as a chance to rally the rest of the EU behind its claim to the territory of 33,000 inhabitants.
It has already secured a right of veto over whether future Brexit arrangements can apply to Gibraltar once Britain has left the EU.
