The brothers, previously identified by the tabloid Expressen as Mensur, 20, and Mentor Alija, 21, received two- and three-year prison sentences respectively for attempted arson from Helsingborg district court in July.
Throughout the proceedings, the Alijas, who are Swedish nationals of Kosovar origin, have continued to deny any involvement in the crime despite the evidence against them.
The attack resulted in a small fire at Vilks' home in Nyhamnsläge, north of Höganäs on the west coast, that later went out by itself.
The Alijas, who are from Landskrona in southern Sweden, were arrested in May after two jackets with a driver's license, bank account information and keys to the brothers' home were found outside Vilks' home.
Both brothers have denied their involvement, even though Mensur Alija reportedly suffered serious burns on the night of May 15th, when the attack occurred. He has claimed he was involved in a barbecue accident.
The attack occured three days after Vilks was attacked during a lecture at Uppsala University.
Vilks has faced numerous death threats and a suspected assassination plot since his drawing of the Muslim prophet with the body of a dog to illustrate an editorial on the importance of freedom of expression.
The cartoon was first published by Swedish regional daily Nerikes Allehanda in 2007
The drawing's publication prompted protests by Muslims in the town of Örebro, west of Stockholm, where the newspaper is based, while Egypt, Iran and Pakistan made formal complaints.
An Al-Qaeda front organisation then offered $100,000 to anyone who murdered Vilks - with a $50,000 bonus if his throat was slit - and $50,000 for the death of Nerikes Allehanda editor-in-chief Ulf Johansson.