The country's air force confirmed the 73-year-old flew to the Maldives with his wife and two security officials.
They arrived in the capital, Male, at around 03:00 local time (22:00 GMT), BBC Sinhala understands.
Mr Rajapaksa's departure ends a family dynasty that has ruled Sri Lanka for decades.
The president had been in hiding after crowds stormed his residence on Saturday, and had pledged to resign on Wednesday 13 July.
A source told the BBC that Mr Rajapaksa will not remain in the Maldives and intends to travel on to a third country.
His brother, former Finance Minister Basil Rajapaksa, has also left Sri Lanka and is said to be heading to the US.
As Sri Lankans awoke to the news, thousands of people took to the streets of the capital, Colombo. Many gathered at Galle Face Green, the city's main protest site. Some listened to fiery speeches at a makeshift stage set up for ordinary people to take the mic.
Punctuated by cries of "Victory to the struggle", the rallying cry of the protest movement, speakers railed against a government and the leaders they feel have failed them.
Some demonstrators were furious about Mr Rajapaksa's departure, seeing a lack of accountability.
"We don't like it. We want to keep him. We want our money back! And we want to put all the Rajapaksas in an open prison where they can do farm work," said protester GP Nimal.
But 23-year-old university student Reshani Samarakoon told the BBC that the former president's exile offered "hope that in the future we can eventually become a developed country, economically and socially".
