It is believed to be the first time during the current migrant crisis in the Mediterranean that refugees have made landfall on UK sovereign territory.
The Ministry of Defence said an agreement with the Cypriot government meant the island authorities would take responsibility for the migrants.
Images released by the MoD show uniformed British personnel talking to two male migrants and a child on the beach and medical staff in attendance at the scene.
RAF Akrotiri has been used for bombing missions against the Islamic State terror group in Iraq and the MoD said the migrant crisis underlines the importance of providing humanitarian assistance in the Middle East.
No details were immediately available about where the 140 occupants of the boats – who include children – had set sail or what their nationalities are.
In a statement, the MoD said: “We can confirm that a number of boats with migrants on board have landed on the shore of RAF Akrotiri in Cyprus. At the moment our key priority is ensuring everybody on board is safe and well and when we can release further details we will.
“We have had an agreement in place with the Republic of Cyprus since 2003 to ensure that the Cypriot authorities take responsibility in circumstances like this.
“Events like this underline why it is important for us to develop a comprehensive approach to the migration crisis working with our international partners to provide humanitarian assistance in Syria and neighbouring countries; to disrupt the trafficking gangs and to address the root causes of instability that cause people to seek a new life elsewhere.”
European Commission president Jean-Claude Juncker has called a special summit of European Union and Balkan leaders in Brussels on 25 October to discuss the migrant crisis.
Austria, Bulgaria, Croatia, Macedonia, Germany, Greece, Hungary, Romania, Serbia and Slovenia have been invited to send representatives.
The emergency meeting was called as Slovenia struggled to cope with a surge of migrants after Hungary completed a razor-wire fence sealing its border with Croatia.
Slovenia’s interior ministry said Croatian authorities were dumping thousands of people a day at its southern border. More than 600,000 migrants have arrived in the EU by boat over the course of 2015 – around 475,000 landing in Greece and 137,000 in Italy – according to figures from the International Organisation for Migration.
The majority of those arriving in Europe are believed to be from Syria, Afghanistan and Eritrea.
Despite its proximity to the Syrian coast – around 100 miles across the sea – Cyprus has received relatively few migrants over the past year.
Meanwhile, the German government is considering using military aircraft to deport rejected asylum applicants.
Germany has seen large numbers of people arriving from several Balkan countries seek asylum this year.