The brothers, from Landskrona in the south of Sweden, faced charges of arson at Helsingborg district court, a crime that carries a penalty of 2-8 years imprisonment.
The prosecutor had sought a six year sentence for the elder brother, a 21-year-old, and four years for his 19-year-old younger brother.
As the court trial opened last Wednesday the 21-year-old defendant described Lars Vilks as "God's enemy, he is the Prophet's enemy, he is the Muslims' enemy."
"He is Islam's greatest enemy right now," he added.
The news agency did not give the brothers' names, but the Expressen tabloid has identified them as Mentor and Mensur Alija, aged 21 and 19.
Vilks has faced numerous death threats and a suspected assassination plot since his drawing of the Muslim prophet with the body of a dog was first published by Swedish regional daily Nerikes Allehanda in 2007 to illustrate an editorial on the importance of freedom of expression.
The brothers, who are Swedish nationals of Kosovar origin, were arrested in May when several of their personal items were found outside the artist's house after it was attacked with Molotov cocktails.
Although the fire blackened some of the house's exterior it went out on its own without causing much damage. The artist was not at home at the time.
Both brothers have denied their involvement, even though Mensur Alija reportedly suffered serious burns on the night of May 15, when the attack occurred.
He has claimed he was involved in a barbecue accident.
The drawing by Vilks 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.