The Prime Minister was speaking to reporters as he travelled to the United Nations General Assembly in New York.
Andy Burnham has agreed to give military support to Saudi Arabia in its struggle against Houthi rebels in Yemen.
The Prime Minister said British planes will provide “defensive” air-to-air refuelling for Saudi jets.
He said he made the decision after discussions with Defence Secretary Wes Streeting and Foreign Secretary Ed Miliband amid fears that the deepening Middle East crisis will add to cost pressures facing British households.
Speaking to reporters as he travelled to the United Nations General Assembly in New York, the Prime Minister said: “We have received a request from the Kingdom of Saudi Arabia for military support.
“On the advice of the Defence Secretary and the Foreign Secretary, last night I agreed to that request for defensive air-to-air refuelling.
“That’s the agreement we’ve given.”
The Iran-backed Houthis have secured a stranglehold over the Bab al-Mandab strait, a maritime chokepoint on the Red Sea, vital for traffic heading to Europe through the Suez Canal.
The Saudis have been targeting the Houthis, while the Yemeni group has been firing missiles at the oil-rich kingdom.
The UK mission will be limited to supporting Saudi aircraft defending the country from attack from drones and missiles rather than supporting strikes against the Houthis.
The use of the Voyager tanker is expected to start within days and the mission will be time-limited, with officials indicating it could last for “weeks”.
The refuelling mission is in addition to the UK Sky Sabre air defence system already deployed in Saudi Arabia.
Mr Burnham said he was “acting to secure the interests of Britain and the wider region because, of course, Saudi Arabia has been experiencing attacks, is looking at potential further disruption, and we need to keep those pathways open, and hence our agreement to the request”.
