Matsis was born in 1933, in Palaiochori, Lefkosia province, the younger brother of Kyriakos Matsis - an EOKA hero. Yiannakis himself took part in the EOKA struggle and was held by the British authorities in Kokkinotrimithia prison. After independence was achieved in 1960, Matsis was elected to the Greek Communal Congress. He was a founding member of the Democratic Rally (DISY) party and was elected four times to the House of Representatives of Cyprus under its banner.
On March 12, 2011, Matsis was arrested by the Turkish military authorities for entering the occupied city of Ammochostos as part of a delegation of Cypriots and members of the European parliament who were investigating the destruction of ecclesiastical property in the Turkish-occupied north of Cyprus. He was released after being fined €90.