Flanked by his wife Margie and Bali governor I Made Mangku Pastika, Abbott bowed his head during the solemn ceremony at a stone monument that honours the 202 people, mostly foreign tourists, who died in the attacks.
Abbott said he was making the visit, after his attendance at a summit on Bali, to "honour the dead, to commiserate with those who were injured on that night and who still bear the scars, physical and mental".
Eighty-eight Australians were among those killed in the attacks by Islamist militants on a nightclub and bar on the party strip of Kuta on the Indonesian resort island.
Abbott's visit to the monument, which stands across from the site of the Sari Club that was attacked in 2002, was his first since becoming prime minister last month and came just days before the 11th anniversary of the attacks.
"The long campaign to provide a measure of justice to the victims of terrorist atrocities overseas is coming to a close," he said, as he announced the compensation scheme.
He said victims of overseas terror attacks and their next of kin could apply for Aus$75,000 (US$70,700) in compensation, in a scheme he said would cost the government about Aus$30 million.
Abbott also recalled that he was in Bali during a second terror attack in 2005, and had volunteered in a local hospital to help victims.
"We have had support all the way through with regard to medical, but there's never been an actual compensation payout," Glenn Cosman, who was hit by shrapnel in the attack on the Sari Club, told ABC radio.
"Many people have always asked that question of me -- what sort of compensation did you get. And the answer has always been nothing."
People will be able to apply for the compensation from October 21 and Abbott said it would benefit around 300 individuals and families.
The scheme to compensate victims of overseas terror attacks was introduced by former Australian prime minister Julia Gillard, but it was not retroactive.
Abbot's plan will also apply to those caught up in other terror attacks, so people affected by the attacks in New York on September 11, 2001 and the 2005 attack in Bali will be able to apply.
Abbott was in Indonesia to attend the Asia-Pacific Economic Cooperation (APEC) summit,