Tradition holds that a church stood at Tännäs as early as the 15th century, and the settlement is first mentioned in records in 1407, which speak of a stave church here. A chapel occupied the site by 1672, and that same year a new church was consecrated by the vicar Hinrik Olofsson-Drake. When a later church was built, the timber from this 1672 building was sold as firewood; its foundations are thought to survive underground in the churchyard, a little south of the present church.
The current building was constructed over a number of years in the mid-1800s. Sources differ slightly on the exact dates: one account gives construction as 1840–1855 with consecration on 10 October 1858, while another gives 1840–1851 with a further rebuilding in 1855, and the same consecration date in 1858. The master builder was Johan Nordell of Los, with local freehold farmers responsible for felling and transporting the timber used in the build; one source credits the architect Johan Adolf Hawerman with the design.
Inside, the chancel painting is described as a work unique to the district, and the church also preserves a number of older items surviving from the two earlier churches on the site. The font takes the form of a christening angel, a sculpted figure holding a baptismal dish. The organ, with fifteen stops and a tremulant, was built in 1960 by Grönlunds Orgelbyggeri.
In 1984 the church underwent a thorough renovation, during which its original decorative colours, painted over in 1958, were uncovered and restored.