The message, which has not been verified, was posted on Boko Haram's Twitter account and is believed to be by the group's leader, Abubakar Shekau.
Boko Haram began a military campaign to impose Islamic rule in northern Nigeria in 2009. The conflict has since spread to neighbouring states.
It would be the latest in a series of groups to swear allegiance to IS.
In the past Boko Haram is thought to have had links with al-Qaeda.
IS took control of large swathes of territory in eastern Syria and across northern and western Iraq last year.
The group aims to establish a "caliphate", a state ruled by a single political and religious leader according to Islamic law, or Sharia. Its leader, Abu Bakr al-Baghdadi, is known to his followers as Caliph Ibrahim.
In the audio message posted on Saturday, the Boko Haram leader purportedly said: "We announce our allegiance to the caliph... and will hear and obey in times of difficulty and prosperity.
"We call on Muslims everywhere to pledge allegiance to the caliph."
-BBC
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