In a 90-19 vote, only three small leftist parties opposed the proposal, which was announced last month by Prime Minister Lars Løkke Rasmussen.
"The brutal and ruthless terrorist organisation IS should meet a powerful response from the outside world," Rasmussen said in a statement, referring to the terror group alternately known as Islamic State, Isis, Isil, IS and Daesh.
Starting from "mid 2016", the Danish contribution will consist of seven F-16 warplanes -- four of them operational at any one time -- a C130J transport aircraft and 400 military personnel, including 60 special forces troops.
Nikolaj Villumsen, a lawmaker for the leftist Enhedslisten (Red Green Alliance), said during the parliamentary debate that Denmark was "once again on its way into a misguided war that could destabilise Iraq and Syria further".
The US heads an international coalition that is carrying out strikes against IS and also providing training and assistance to forces fighting the jihadists in both Iraq and neighbouring Syria.
Denmark is a member of the coalition but previously only had a mandate to intervene in Iraq.
From October 2014 until October 2015, it had seven F-16s fighting IS in Iraq.
Denmark currently has around 120 troops stationed at the Al-Asad air base some 180 kilometres (110 miles) northwest of Baghdad, where they have been training Iraqi soldiers and Kurdish security forces.