The church takes its name from Queen Hedvig Eleonora and was built to serve Norrköping's German-speaking residents, who had worshipped for decades in borrowed premises before receiving permission from Duke Johan in 1613 to form their own congregation. Funds were slow to gather, and it was not until 1670 that the foundation stone was laid, with the building finally consecrated in November 1673. A tower was added in the 1690s, funded partly through donations of roofing copper and a bequest from a local benefactor.
Disaster struck in 1719 when Russian troops burned much of Norrköping during the Great Northern War, destroying the church almost entirely. Rebuilding drew on contributions from Sweden and abroad, and contemporary accounts credit the tireless efforts of the parish's own pastor in securing support; the restored church was said by some to be even finer than before the fire. The building's interior is notable for its wide vaulted ceiling, formed of three bays supported without the need for internal pillars.
Among the church's furnishings is a pulpit dating from the 1720s, believed to have been made in Germany and donated by the merchant Andreas Spalding and his wife Anna Bandholt; it is decorated with a sun motif bearing the Hebrew letters of the divine name. The font dates from 1608 and originally stood in the chapel of Stegeborg Castle before being given to Hedvigs kyrka in 1733. The altarpiece, depicting the risen Christ with the doubting Thomas, was painted by Pehr Hörberg in 1791.
During the Riksdag of 1799–1800, held in Norrköping, the church served as a meeting hall for the Swedish nobility. Later renovations altered the interior considerably: a sacristy, new pews, an organ loft and a new organ were added in the early 1860s, and further changes followed in the 1890s. A 1959 restoration returned the exterior to its original seventeenth-century appearance, and in 1996 the altar rail and platform were removed to make it easier to hold communion.
The church's organ has a long and layered history, beginning with an instrument bought from Hamburg in 1680 that was destroyed in the 1719 fire; the present organ has been rebuilt and altered several times since 1792, most recently in the early 2000s. Three bells hang in the tower, cast in 1720, 1930 and 1965 respectively. In the porch, visitors can see modern stained glass by the artist Jan Brazda.