Before Týr, Heri Joensen and Gunnar H. Thomsen formed their first band, Cruiser, at the age of seventeen. Streymoy also played with them for a short while. They later changed their name to Wolfgang. Although neither band released any albums, Wolfgang, who are still active, recorded an undisclosed amount of songs that, according to Joensen are "pretty much ready to release.
Týr formed in January 1998. Heri Joensen met his old bandmate, Kári Streymoy, at a party in Copenhagen, Denmark. Joensen suggested to Streymoy that they should meet up and jam. Streymoy initially declined, but later took him up on his offer. They were soon joined by another former bandmate, bassplayer Gunnar H. Thomsen, making the duo a trio.
They began making music which was heavily inspired by Norse mythology, Faroese traditional music, and heavy metal music in general. According to the band's frontman Heri Joensen:
"Týr's musical mission is to break down the walls that are erected between all the kinds of metal that have arisen over the years. Power-, doom-, black-, progressive-, gothic-, Viking-, folk-, ethnic- and epic metal. Walls and labels do nothing but fill people with prejudice."
Singer Pol Arni Holm and guitarist Jón Joensen (Heri Joensen's brother) were part of the band while they recorded How Far to Asgaard but left soon after its release. Terji Skibenæs joined after Jón Joensen had left the band. Allan Streymoy (Kári Streymoy's brother) took over singing duties for a brief time during which they released the single "Ólavur Riddararós". After Allan left Heri Joensen took over the vocals. It was this line up which recorded Eric the Red.
Skibenæs left the band for awhile after the release of Eric the Red. The band played as a trio for some time. In the summer of 2004 they were joined by Icelandic guitarist Ottó P. Arnarson for a very brief time. When Arnarson left, Skibenæs came back.
Kári Streymoy had a back injury in January 2008, which made him unable to tour until October the same year. Amon Djurhuus, a Faeroese drummer and student of Kári Streymoy, played the drums on the European part of the Paganfest, Merlin Sutter from Eluveitie filled for him on the US part and Daniel Ryan from Gigan on the Canadian part. After that for the festival tour in Europe Amon Djurhuus filled for Kári again. In October 2008 Kári Streymoy was ready to go again for the Ragnarök's Aaskereia Festival Tour.
In April 2008, Týr and other performers on the folk metal festival Paganfest were subject to accusations of being Nazis, racists and fascists from the German BIFFF (Berliner Institut für Faschismus-Forschung und Antifaschistische Aktion) led by Peter Kratz. Ville Sorvali of Moonsorrow and Heri Joensen of Týr issued a joint video statement to refute these accusations, noting that the bands are in no way connected to far-right groups and actually are against fascism.
This incident is often said to be have been sparked by the over-cautioness of the BIFF with pagan and Nordic symbols and folklore, as some of these symbols were used by the Nazi party.