The undefeated 24-year-old, who is also the reigning British and Commonwealth champion, will feature on the undercard of Dereck Chisora's rematch with Joseph Parker at the AO Arena on Saturday, December 18.
It will be the second defence of a belt he won in March when he obliterated Frenchman Karim Guerfi in the first round.
The former Meadowbank amateur then made a successful first defence with a fourth-round stoppage of Vincent Legrand in Belfast in August, although McGregor was knocked to the canvas for the first time in his professional career in round two.
The Scot, who is trained by coach Ben Davison, has also signed a multi-fight co-promotional deal with Matchroom Boxing and Probellum that, he believes, will help him reach his goal of becoming world champion.
“I’m absolutely delighted to be getting back in the ring defending my European title against Narek Abgaryan,” McGregor said.
“This is another step closer to me becoming a world champion. I have the best team possible and I believe with Matchroom and Probellum backing me, I can win world titles at multiple weights.”
Matchroom Sport chairman Eddie Hearn added: "I’m delighted to welcome reigning European, British and Commonwealth bantamweight Champion Lee McGregor to the team.
“Lee has become one of the hottest young talents in world boxing. We look forward to watching him perform in Manchester and then the huge all-Scottish rematch with Kash Farooq in early 2022."