The video, produced by IS's Al-Hayat Media Centre, shows television news footage from the night of the attacks, as well as clips of the assailants delivering their final messages in French and Arabic.
They call on Muslims living in Europe to carry out lone-wolf attacks and, in particular, threaten Britain.
Images of French President Francois Hollande and British Prime Minister David Cameron are also used, both with targets superimposed on them.
Referring to the 70-nation coalition fighting IS, purported attack ringleader Abdelhamid Abaaoud warns that "the more you wage war against the Islamic State, the more it will expand... for we are terrorists."
But Hollande, who is on a visit to India, dismissed the threats.
"Nothing will deter us, no threat will make France waver in the fight against terrorism," he told reporters.
And Cameron's office said the video showed "an appalling terrorist group that's clearly in decline and in retreat."
In a report released on Monday, the European police agency Europol warned IS was planning more attacks on soft targets in the EU.
Europol chief Rob Wainwright said IS had "developed a new combat style capability to carry out a campaign of large-scale terrorist attacks on a global stage -- with a particular focus in Europe."
- 'Incredible level of planning' -
The video confirms for the first time that IS trained attackers and sent them to carry out an assault in the West. Until now, the group has mostly focused on using propaganda to inspire supporters from afar to strike.
Seven men in military fatigues are shown outdoors, in what appears to be a desert setting, with victims whom they later shoot or behead, while another is seen carrying out target practice.
Abaaoud, who was killed in a police raid after the attack, is the only one speaking indoors. He is identified by his battlefield name Abu Umar al-Baljiki, as are the other men.
The video "portrays an incredible level of planning and integration of the IS propoganda apparatus from a very early stage of planning," said Charlie Winter, a researcher at Georgia State University who monitors jihadist propaganda.
"These executions would have taken place months ago... it shows a high degree of patience," he told AFP.
Raffaello Pantucci of the Royal United Services Institute (RUSI) in London said the planning behind the video "specifically highlights how this was a plot that was directed by core IS."
With French and Arabic songs playing in the background, the video calls for the murder of Westerners, lyrically chanting the names of the Paris streets Charonne and Voltaire where attacks took place.
It also praises Amedy Coulibaly, who killed four hostages at a Jewish supermarket in January 2015, two days after the Kouachi brothers staged a deadly attack on the Charlie Hebdo magazine, killing 12.
- Iraqis at the stadium? -
It is still not clear how many people were involved in the assault on Paris in which seven assailants blew themselves up or were shot dead by police.
Two men who blew themselves up outside the national stadium and were found with fake Syrian passports, have not yet been identified and are believed to be the two Iraqis shown in the video.
Abaaoud, thought to have previously fought in Syria, was killed in a shootout with French police days after the attacks, alongside another man seen in the IS video, who blew himself up.
Winter said the stark difference between Abaaoud's appearance in a small room and that of the other men -- carrying out scripted atrocities with a microphone attached to their lapel -- could be interpreted as a sign that he "was not meant to die or be detected by security forces."