The pledge, attributed to Boko Haram leader Abubakar Shekau, was made in an audio recording posted on the group's twitter page on Saturday, but it could not be immediately verified, Reuters reported.
"We announce our allegiance to the Caliph ... and will hear and obey in times of difficulty and prosperity," SITE quoted Boko Haram as saying in a video purporting to be from the Nigerian rebel group.
The video script identified the caliph as Ibrahim ibn Awad ibn Ibrahim al-Awad al-Qurashi, who is better known as Abu Bakr al-Baghdadi, the leader of ISIL, which controls large swaths of territories in Iraq and Syria.
Baghdadi has already accepted pledges of allegiance from other armed groups in the Middle East, Afghanistan, Pakistan and north Africa.
Speaking to Al Jazeera, Boko Haram expert Aliyu Musa said: "It's not the first time Abubakar Shekau has done this - remember, when they started taking parts of Nigeria last year, he did proclaim support for ISIL."
Boko Haram has been waging a six-year military campaign to carve out a state in northern Nigeria.
On Saturday, three bomb blasts killed at least 51 people in the northeastern Nigerian city of Maiduguri in the worst attacks there since Boko Haram fighters tried to seize the town in two major assaults earlier this year.