He was the prime minister of the Faroe Islands from 2004, starting shortly after the general election of 20 January 2004, until 26 September 2008, when a new coalition took office.

He was a member of the Danish Folketing representing the Faroe Islands from 11 March 1998 until 20 November 2001.

Jóannes Eidesgaard was born on 19 April 1951, in Tvøroyri on the island of Suðuroy, where he later became a senior-school teacher.

On 3 February 2004 Jóannes Eidesgaard was elected prime minister and therefore became head of the government in the Faroe Islands.

On 30 September 2008 shortly after making the 2009 Faroese budget public, Jóannes Eidesgaard was admitted to hospital after feeling chest pains.