The historical record is unfortunately quiet on when and how the conversion of Sweden occurred. Paganism held out there for an especially long time compared to the rest of Scandinavia, but by the twelfth century, the country was mostly Christian.
According to the eleventh-century historian Adam of Bremen, King Erik the Victorious, who ruled Sweden in the late tenth century, converted to Christianity but eventually fell back into paganism. Erik’s son Olaf, who ruled from roughly 995-1022, seems to have been a Christian, as evidenced by coins minted in his name that bear Christian features. Olaf seems to have founded a bishopric at Skara in western Sweden. Olaf’s son Anund ruled from about 1022 to 1039, and was certainly Christian, since he was given the Christian name James. Adam claims that during Anund’s reign, Christianity was widespread in Sweden. England, Germany (Hamburg-Bremen), and Poland all vied for influence in Sweden’s Christian institutions, such as they were.
According to The Saga of Erik the Red, there were Christians among the people whom Erik the Red brought to Greenland to settle it in the late tenth century. In 999, Leif, the son of Erik, was converted to Christianity by Olaf Tryggvason. He sailed to Greenland with a priest to convert the people. Erik himself was initially skeptical, but Thjodhild, Erik’s wife and Leif’s mother, embraced it. She refused to let Erik sleep in the same bed as she until he relented and accepted the new religion, which he eventually did.
Regardless of the historicity of the particulars of this story, a tiny church was indeed built in Brattahlid, Erik’s settlement, in the eleventh century. Adam of Bremen, writing in the 1070s, corroborates the notion that Christianity had reached the Greenlanders and was making inroads among them by that time.