Eames did articles at the firm of Slater and Gordon, and was admitted to the Victorian Bar in 1969.[1]
In the 1970s he joined the Central Australian Legal Service as its principal Solicitor, and was then seconded to the Central Land Council in Alice Springs where he pioneered all early land claims made under the Aboriginal Land Rights Act, Northern Territory, 1976 and the passage of the legislation itself, before heading to the bar in Darwin.
In 1980, he was admitted to the bar in South Australia, joining the independent bar in 1984. Eames was a member of Hanson Chambers from 1987 to 1991, and took silk as a Queen's Counsel in South Australia in 1989 and in Victoria in 1990. During this time he worked as a barrister in two Royal Commissions: the McClelland Royal Commission (1985) into British nuclear testing in Australia, and the Royal Commission into Aboriginal Deaths in Custody (1987–1991).[1]
On 26 May 1992, Eames was appointed as a judge of the Supreme Court of Victoria. On 15 March 2002 he was appointed a judge of the Court of Appeal and served until 2007.[4]
Eames was appointed as an Acting Judge of the Supreme Court of the Northern Territory between 2007 and 2009.[2][5]
In December 2010, Eames was appointed Chief Justice of the two-member Supreme Court of Nauru. In January 2014, the Chief Magistrate of Nauru, Peter Law, issued an injunction to prevent the deportation of three foreign nationals. Law was fired by Nauru President Baron Waqa and himself deported. Eames, in Australia at the time, issued an injunction to prevent the deportation of Law, however Law was deported. The Nauru government cancelled Eames' visa which prevented his return to Nauru,[6] and he resigned two months later.[3] The incidents involving Law and Eames were criticised by Mathew Batsiua a member of Nauru's Opposition and precipitated a government crackdown on opposition.[7]