Astro Labe, 38, admitted in court on Thursday to a charge of causing harm to a Commonwealth official. The incident happened in Hobart in September.
At the time Mr Abbott blamed the head-butt on his opposition to same-sex marriage, a claim later denied by Labe.
The Hobart man, a self-proclaimed anarchist, said he had been motivated by “personal hatred” for Mr Abbott.
A Hobart court heard Labe had followed Mr Abbott for 250m (820ft) before deliberately assaulting him, the Australian Broadcasting Corp reported.
In September, Mr Abbott said he offered a handshake to Labe before being pulled in for a “Liverpool kiss”, for which he suffered a swollen lip.
Labe faces a maximum penalty of two years’ jail and a A$25,000 (£14,000, $19,000) fine. He will be sentenced in March. (Courtesy BBC)