"We announce to you to the good news of the expansion of the caliphate to West Africa because the caliph... has accepted the allegiance of our brothers of the Sunni group for preaching and the jihad," IS spokesman Mohammed al-Adnani said in the message, using the Arabic name for Nigeria's Boko Haram extremist group.
In the tape of some 30 minutes, Adnani urges Muslims to join militants in West Africa and played down "victories" by the US-led coalition and Iraqi forces against his group.
The Sunni radical Sunni movement has seized large swathes of Iraq and Syria and declared an Islamic "caliphate" there. It has also drawn expressions of allegiance from jihadists in Egypt and Libya.
On Saturday, an audiotape attributed to Boko Haram leader Abubakar Shekau said "we announce our allegiance to the Caliph of the Muslims, Ibrahim ibn Awad ibn Ibrahim al-Husseini al-Qurashi," referring to IS leader Abu Bakr al-Baghdadi.
Security analysts have said that pledge may only have propaganda value in the short term but could lead to closer links in the future.
Shekau has previously mentioned Baghdadi in videos but stopped short of pledging formal allegiance.
But there have been increasing signs that the Nigerian militants, whose six-year insurgency has claimed more than 13,000 lives and left 1.5 million people homeless, have been seeking a closer tie-up.
IS's Adnani said Muslims must support Boko Haram in West Africa, and claimed that the Islamic State was growing in strength and expanding.
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"Our caliphate is resisting and it is advancing in the right direction. We are fighting the Crusaders and the rafidah (Shiites) and day by day the Islamic State is becoming strong," he said.
The tape's release comes as US Security Council diplomats are drafting a resolution to shore up a regional force fighting Boko Haram, and as Iraqi forces were tightening the noose on IS in Tikrit.
Iraqi forces entered IS-held Tikrit, in the northern province of Salaheddin, on Wednesday after a 10-day push to wrest the city back from the jihadists.
A combination of army, police and volunteer forces moved into northern and southern Tikrit, the hometown of former Iraqi president Saddam Hussein and a main IS stronghold after making major gains around the city.
But Adnani said IS "continues to resist.... and the victories proclaimed by the coalition are only illusions", claiming that only "inches of land" in Iraq had been recaptured by loyalist forces.
And he insisted that the group is "sure of its victory" regardless of the challenges it is facing.
"God is on our side and give us the strength to combat this armada of Crusader countries," he said.
For months, IS has been targeted with air strikes from a coalition led by the United States and already suffered territorial setbacks in Syria and Iraq.