He studied theology, was ordained priest and for a number of years served as pastor at Oddi, S Iceland, and later in Akureyri.
In addition to his own works, which include many hymns, Matthías was a prolific translator, especially from English and the Scandinavian languages.
His translations from Shakespeare include Hamlet, Macbeth, Othello and Romeo and Juliet.
Matthías's popular comedy, "Skugga-Sveinn", which premiered in 1860, is often hailed as Iceland's first successful performed play.
He died in Akureyri, where his house, Sigurhæðir [is], is now a museum, devoted to his life and work.