Sri Lankan President Gotabaya Rajapaksa has announced he will step down after protesters stormed his official residence and set the prime minister's house on fire.
Neither the PM nor the president were in the buildings at the time.
Hundreds of thousands descended on the capital Colombo, calling for Mr Rajapaksa to resign after months of protests over economic mismanagement.
Mr Rajapaksa will step down on 13 July. PM Wickremesinghe has agreed to resign.
The speaker of parliament said the president decided to step down "to ensure a peaceful handover of power" and called on the public to "respect the law".
The announcement triggered an eruption of celebratory fireworks in the city.
One protester, Fiona Sirmana, who was demonstrating at the president's house, said it was time "to get rid of the president and the prime minister and to have a new era for Sri Lanka".
"I feel very, very sad that they didn't go earlier because had they gone earlier there wouldn't have been any destruction," she told Reuters.
Sri Lanka is suffering rampant inflation and is struggling to import food, fuel and medicine amid the country's worst economic crisis in 70 years.
It has run out of foreign currency and has had to impose a ban on sales of petrol and diesel for private vehicles, leading to days-long queues for fuel.