Lors Doukaev was found guilty of attempted terrorism and weapons possession and faces permanent expulsion from Denmark after serving his sentence.
The Copenhagen court heard that Doukaev, 25, planned to send a letter bomb to the offices of Denmark's Jyllands-Posten newspaper in retaliation for publishing 12 caricatures of the Prophet Mohammed in 2005.
However, the plan failed as Doukaev was arrested in a Copenhagen park in September 2010, following a minor explosion in a nearby hotel. He admitted to accidentally setting off the bomb, and was the only person injured in the blast.
He claimed he had been disarming the device, which he intended to use to protect himself from other Chechens while staying at the hotel. The court did not accept his explanation.
Among the evidence presented against Doukaev were envelopes with the address of the newspaper written on them, as well as computer records showing he had visited the newspaper's website while in Copenhagen.
In addition, the prosecution said the bomb was built according to a manual found in a flat in Liege, Belgium, where a friend of Doukaev's lived, along with videos promoting Islamic jihad.
His defence argued he was visiting the website to read job advertisements, adding there was no evidence to support the charges he was seeking to avenge publication of the drawings.
Defence lawyer Niels Anker Rasmussen said previous terrorism trials had resulted in similar sentences, but only in cases involving much larger quantities of explosives.
Doukaev did not accept the terror charges and may appeal the sentence.
This is the second sentence in four months in terror cases involving Jyllands-Posten. In February, a Somali immigrant in Denmark was sentenced to 9 years in prison for attempting to kill Kurt Westergaard, one of the artists responsible for the caricatures.