It is understood he has agreed a contract tying him to the Scotstoun club until the end of the season and will join up with the Warriors after spending Christmas with his family in Fiji.
Nakarawa is a free agent having been released by Racing 92 after he returned to the club 16 days late following the World Cup.
Bayonne claim the lock forward had verbally agreed to join them but had changed his mind and signed for Glasgow.
Nakarawa signed his first professional contract when joining the Warriors in 2013 and was a hugely popular player with the Scotstoun club, helping them win the Pro12 title in 2015. He left in 2016 to join Paris-based Racing 92.
A statement posted yesterday by Bayonne president Philippe Tayeb said: “After giving a verbal agreement to our proposal that validated his arrival on Saturday, 7 December, Leone Nakarawa has reversed his decision and decided not to follow up on the offer we made him.
“We would have liked to welcome this player into our squad but we fully respect his choice to join his former club Glasgow Warriors.”