The men were arrested in 2010 for planning to blow up the offices of the Jyllands-Posten daily that had published 12 caricatures of the Muslim prophet in September 2005.
In January, an Oslo district court sentenced Norwegian national Mikael Davud, a member of China's Uighur minority considered the mastermind of the plot, to seven years behind bars.
It handed Shawan Sadek Saeed Bujak, an Iraqi Kurd residing in Norway, a three-and-a-half-year term.
While the appeals court upheld the verdict Thursday, the decision concerned only the men's guilt and not the length of their sentences.
The court failed to come to a decision over the guilt of a third man, David Jakobsen — an Uzbek arrested at the same time as Davud and Bujak — according to Norway's NRK broadcaster.
Jakobsen was acquitted in January of the most serious charges but was sentenced to four months' jail for helping the others procure bomb-making material.
The appeals decision came after French weekly Charlie Hebdo, which reproduced the Danish caricatures in 2006 and whose offices were fire-bombed last year, published new cartoons featuring crude depictions of the prophet.
Their publication comes against a background of violent protests across the Muslim world, which first erupted early last week over an anti-Islam film made in California and posted on the internet.