The move raised hope for some of the more than 120,000 tourists stranded after a surge in activity at Mount Agung had grounded hundreds of flights since Monday, sparking travel chaos and forcing the evacuation of villagers living in its shadow.
Airport officials cautioned that the airport could shut again if winds change direction once more and endanger flights.
Ash is dangerous for planes as it makes runways slippery and can be sucked into their engines.
Domestic carrier Garuda said it would start flights to several cities across the vast archipelago nation this evening, while AirAsia was set to fly to the Malaysian capital Kuala Lumpur.
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All other international flights were on standby.
Australian tourist Ebra Syllivan was overjoyed at the prospect of getting back home.
"I didn't know it was going to reopen today -- we just came here because our flight was (originally scheduled for) tonight and we've booked out of our motel," she said at the airport.
Mount Agung could produce a major eruption at any moment, officials have warned.
Tens of thousands have already fled their homes around the volcano -- which last erupted in 1963, killing around 1,600 people -- but as many as 100,000 will likely be forced to leave in case of a full eruption, disaster agency officials have said.
Experts said Agung's recent activity matches the build-up to the earlier disaster, which ejected enough debris -- about a billion tonnes -- to lower global average temperatures by around 0.3 degrees Celsius for roughly a year.
"Activity remains high and we are still on the highest alert level."
Roadside signs that read "Volcanic danger zone. No entry!" underscored the potential risks of staying behind.
There is a 10 kilometre exclusion zone around Agung, which is 75 kilometres from the beachside tourist hub of Kuta.
As of today around 440 flights had been cancelled since the start of the week.
The airport on nearby Lombok island -- also a popular tourist destination -- has opened and closed several times in the past few days. It is currently open.
"We decided to take the bus because in this island we are very nervous and we want to stay in another island, we want to be in Java," said Sofia Maria, a 24-year-old Russian tourist on her way to Jakarta.
The majority of Bali's tourists are Chinese, followed by Australians, Indians, Britons and Japanese, according to the immigration office, which added that nearly 25,000 foreigners live on the small Hindu-dominated island.
Agung rumbled back to life in September, forcing the evacuation of 140,000 people living nearby. Its activity decreased in late October and many returned to their homes.
However, on Saturday the mountain sent smoke into the air for the second time in a week in what volcanologists call a phreatic eruption -- caused by the heating and expansion of groundwater.
So-called cold lava flows have also appeared -- similar to mud flows and often a prelude to the blazing orange lava of popular imagination.
Last year seven people were killed after Mount Sinabung on the western island of Sumatra erupted. A 2014 eruption at Sinabung killed 16.
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