The Cypriot government said those who had both Covid jabs could travel there without restrictions from 1 May, according to the BBC.
But this is more than two weeks before the earliest date those in England will be able to go abroad for holidays.
It is not clear how tourists will be required to prove they have had both vaccine doses.
Cyprus’s deputy tourism minister, Savvas Perdios, said the country would allow Britons who had been given vaccines approved by the European Medicines Agency (EMA) the right to enter without the need for a negative test or to quarantine.
Tourists would be required to have had their second dose at least seven days before travelling, the minister added.
Currently the Pfizer-BioNTech, Oxford-AstraZeneca and Moderna jabs have been approved for use by the EMA.
British tourists make up the largest group of visitors to the island, and made more than a million trips to Cyprus in 2019, according to the Office for National Statistics.
Cyprus has already struck a similar agreement allowing Israeli tourists to enter the country from 1 April.
Greece has also agreed to admit visitors from Israel who can prove their status with the Israeli “green” digital certificate.
The UK government has not yet approved any vaccination certificate but Cabinet Office Minister Michael Gove is leading a review into possible measures.
Simon Calder, travel editor at the Independent, said, with the UK’s vaccine programme ahead of the rest of Europe, the British holidaymaker was going to become “quite appealing to countries who are working out how to rebuild their tourist industries while at the same time minimising risk”.
Although family members might have different vaccination statuses, potentially meaning only some were able to travel unrestricted, he told BBC Breakfast he thought there would be “a way found”.
Mr Calder said it was possible Cyprus would reflect its travel rules from last summer when visitors were able to get a test three days before their flight and noted that under-12s are excluded from the current travel restrictions.
But foreign leisure travel will still be barred for people in England at the beginning of May, with Prime Minister Boris Johnson saying the earliest Britons could jet away is 17 May.
This is dependent on various factors related to the coronavirus pandemic, such as vaccine rollouts and the prevalence of Covid-19 variants.
