He was studying divinity when he met a young violinist and composer, Johan Svendsen.

Sveinbjörn went to Copenhagen, but later carried on to Leipzig where his teacher was Carl Reinecke.

Consequently, Sveinbjörn gained a far higher level of musical education than other musicians in Iceland at that time.

As the musical opportunities were limited in Iceland at the end of the 19th century, Sveinbjörn moved to Edinburgh.

His composition pieces were mostly melody songs or poetical chamber music in the spirit of Mendelssohn.