The group said its supporters had "occupied" the iconic bridge and that six trained climbers had abseiled from it.
The six who abseiled were later removed from the bridge and also arrested.
The 15 people arrested include ten men aged 70, 56, 48, 39, 38, 37, 34, 32, and two aged 27, as well as five women, aged 21, 26, and three aged 28.
Several others managed to climb over the edge and rappel under the main deck of the bridge.
They were all conditionally bailed, charged with climbing the bridge and willfully preventing the free passage of a person/vessel.More news: De Blasio Holds Campaign-Style Rally In Trump Tower
Police arrested 10 people earlier this morning before arresting the final three, who were attached to ropes beneath the bridge, about 9.30am, bringing the operation to a close.
All 13 people have been taken to Surry Hills and Day Street Police Stations.
No charges have been laid yet.
"6 activists have just scaled the Sydney Harbour Bridge to call on Scott Morrison to declare a #ClimateEmergency" and asked people to sign a petition in support of them", said a post on social media from Greenpeace.More news: Madonna rejects calls for Tel Aviv Eurovision boycott
The protest began around dawn, with a number of people involved.
"This is a climate emergency and the prime minister must listen to Australians whose lives are already affected", said David Ritter, chief executive officer of Greenpeace Australia.
Greenpeace have said that the protestors were calling on Prime Minister Scott Morrison to "declare a climate emergency"..
Coal is the biggest cause of climate change: we need 100% renewables, stat.
A group of indigenous Torres Strait islanders lodged a formal complaint against the Australian government at the United Nations on Monday, claiming that their climate inaction violated their basic human rights.More news: AEW Coming To TNT