The name Sveneby is thought to derive either from the personal name Sven or, perhaps more plausibly, from the term "sven av vapen", a rank denoting a powerful man just below a knight. The church stands at the northernmost tip of Lake Östen, once recorded as Odens sjö (Odin's lake).
The surviving western part of the nave belongs to the original 12th-century building, and the roof trusses may also be medieval. During a 1970s renovation, a small defensive slit was found in the south façade's gallery level; radiocarbon dating of its window frame suggested a date as early as 1005, though such early dating should be treated with some caution given the building's otherwise 12th-century origins.
The cross-shaped transepts (korsarmar) to north and south are generally thought to have been added in the 1600s. By the 1670s the church is recorded as having had a straight-ended chancel, north and south transepts, a small western porch and a central bell tower, an arrangement shown in an early drawing from around 1700. In 1746 the chancel was widened and heightened, transforming the building into a hall church (salkyrka), while a sacristy was added and the western porch enlarged. A separate timber bell tower was built in the 1750s.
Among the church's furnishings is a triumphal crucifix from the 1120s, one of the oldest objects in the building, alongside a 13th-century crucifix. The medieval font has a cubic bowl with a drainage hole, a practical detail typical of fonts used for full immersion or the outflow of consecrated water. A carved figure said to depict Bishop Erasmus in a tar cauldron adds an unusual and slightly macabre note among the church's older furnishings. A small chamber organ with six stops was built in 1983 by Smedmans Orgelbyggeri of Lidköping.