"[The] Islamic State [of Iraq] has fulfilled what it promised you," Taimour Abdulwahab allegedly wrote in the will posted by a jihadist on the Shumukh al-Islam website, according to the SITE (Search for International Terrorist Entities) Intelligence Group, a US-based for-profit entity.
The Swedish capital was hit by twin explosions on Saturday -- a suspected suicide attack and separate blast -- targeting Christmas shoppers in a busy pedestrian area of the city. A man investigators suspect may have been the bomber was killed, while the other explosion nearby injured two people.
Shumukh al-Islam named Abdulwahab as the man responsible for the blasts, although Sweden's intelligence agency Säpo has refused to comment on the claim.
The late chief of the self-proclaimed Islamic State of Iraq, Abu Omar al-Baghdadi, had called in an audio message in September 2007 for reprisals in Sweden for the cartoons of Islam's prophet Mohammed by Swedish artist Lars Vilks.
Baghdadi also offered cash for killing the cartoonist and named Swedish companies such as Ericsson, Ikea and Volvo as potential targets to harm Sweden's economy.
British media reported on Monday that Abdulwahab had studied at the University of Bedfordshire in Luton, around 50 kilometres northwest of London, and had been living in the town in recent years. His wife and children were reportedly still living in Luton, The Daily Mail and The Daily Telegraph reported.