The accused, Nino Koehler, had apologized during his trial to the imam and his family. No one was hurt in the attack.
The bomb damaged the door of the Iman mosque while the family were inside on Sept 26, 2016.
That same evening, the accused planted another homemade pipe bomb that slightly damaged a convention center in the city, which was days away from hosting festivities to mark 26 years since the reunification of east and west Germany.
The attacks in Dresden, the capital of Saxony state and the birthplace of the anti-Islam Pegida movement, shocked Germany.
The city's district court found Koehler guilty of attempted murder, setting off explosives and attempted aggravated arson. The judge sentenced him to nine years and eight months in jail, AFP reported.
Prosecutors accused him during the trial of harboring racist and Islamophobic motives, and media reports said he had railed against "lazy Africans" and "criminal foreigners" at a past Pegida rally.
Koehler, who was arrested in December 2016, told the judge that he never meant to hurt anyone.
Saxony, in Germany's ex-communist east, has become a hotspot for far-right protests and hate crimes after more than a million asylum seekers arrived in Europe's biggest economy since 2015.
The Saxony town of Chemnitz has been rocked by racist violence this week, after far-right mobs took to the streets to protest the fatal stabbing of a German man, allegedly by an Iraqi and a Syrian.
Pegida and the Alternative for Germany (AfD) groups have called for a "silent march" in Chemnitz from Saturday in memory of the stab victim, adding to midweek protests by far-right demonstrators to protest Chancellor Angela Merkel's immigration policy.
Leftist movements have called a counter-march.
The ongoing tensions have forced the postponement of Saturday's second division football match between fallen giants Hamburg and Dynamo Dresden in Dresden, some 80 km from Chemnitz, owing to extra police being diverted to cover nearby protests.
The German football federation said the interior ministry had cited the expected demos by far right groups in nearby Chemnitz as the reason for postponing a game that some 30,000 fans already had bought tickets for.
A new match date has yet to be set.
Saxony state police do not expect more than a few thousand demonstrators but have drafted reinforcements just in case after the violence of the past week which saw a racist mob chase foreigners through the streets as hard right and left protesters clashed.
Police had come in for some criticism for their handling of the previous demonstrations after the situation boiled over.