The origins of the church lie in the political aftermath of the 1809 Treaty of Fredrikshamn, which split the region of Tornedalen and left the old church at Turtola on the Finnish (then Russian) side of the border. To discourage the Swedish-side population from continuing to attend services across the new frontier, the Swedish parliament granted funds for a chapel in the Swedish part of Turtola, a settlement that later took the name Svanstein.
The present church was completed in 1865, designed by the architect Ludvig Hawerman in a restrained classical style. It was built as a timber hall church with a chancel and an attached sacristy to the east, and was originally painted red. The builder was Matti Havela, from Pello in Finland, said to have been the great-grandfather of the Swedish provincial governor Ragnar Lassinantti.
The church was substantially altered in 1927–1929 under architect Olof Lundgren, when a tower with a lantern was added. At the same time a gallery was installed inside, and decorative paintings were added to the ceiling and above the windows. A further renovation in 1974, overseen by Bertil Franklin, gave the exterior its current pink colour, shortened the gallery, lowered the chancel floor to match the rest of the nave, and replaced some of the furnishings.
Among the church's furnishings is an altarpiece depicting Christ on the cross, donated during the 1927–1929 restoration; it is normally kept in the sacristy but is traditionally hung above the altar during Lent. The altar itself is otherwise marked by a plain wooden cross, added in the 1974 renovation to replace an earlier altarpiece. The single-manual organ was built by Grönlunds Orgelbyggeri and installed in 1964.