The change comes into force on Monday to coincide with the half-term break.
Many families cancelled plans to visit Spain during the school holiday due to its ban on UK children over 12 who are not fully vaccinated.
The UK, including Scotland, significantly eased its rules for arriving travellers at 4am on Friday.
People who are fully vaccinated no longer need to take a post-arrival lateral flow test, which typically cost about £20 each.
The requirement for unvaccinated arrivals to self-isolate has been dropped, but they still need to take tests.
Aviation minister Robert Courts said the changes were “a long time coming”.
He told LBC radio: “We’ve had a very difficult time both for the travel industry and for people who rely on travel – people who need to go on holiday, people who need to work on their businesses, people who haven’t seen their friends and family for so long.
“And so this has been a long road, but due to the success of the vaccination programme, I am really glad to be able to bring you this news this morning that we are taking the trouble out of travel.
“We are making it much simpler for people to be able to get about, to go on holiday and to see all those friends.”
Hundreds of thousands of people in the UK are embarking on foreign trips during half-term.
Turkey, Egypt and Portugal are among the most popular short-haul destinations, while departures to the US state of Florida, Dubai, Mexico and the Caribbean have sold well for longer-haul holidays, according to the travel trade organisation Abta.
Ski resorts in France, Italy and Switzerland are also in demand.
Spain’s ministry of industry, trade and tourism said from Monday that children aged 12 to 17 arriving from the UK will only be required to show evidence of a negative PCR test taken within the past 72 hours of arrival.
UK adults will continue to need to be fully vaccinated to enter Spain.
The country’s minister for trade, industry and tourism, Reyes Maroto, said: “We are committed to making travel to Spain a safe and easy experience for our visitors, especially for families travelling with children.”
Steve Heapy, chief executive of airline and tour operator Jet2, said: “This is very welcome news for families who want nothing more than to holiday in their favourite Spanish destinations.
“We are pleased to see the Spanish government taking positive action to welcome more arrivals from the UK and we know that this will lead to an increase in bookings.”
Jet2 said bookings for all destinations over the past four weeks for half-term trips were 30 per cent higher than during the same period in 2020, which was before the pandemic hit the aviation industry.
Stansted Airport told Abta it is expecting about 200,000 passengers to depart between Friday and February 18.
Cross-Channel train operator Eurostar said more than 125,000 people are booked to travel between the UK and the Continent during the school holiday.
The busiest day will be Friday, when more than 16,000 passengers are booked to travel. Several services are sold out.