When he was seven years old, he fled Baghdad in the middle of the night alongside his family, then moving to Syria, where Amir saw his father for the first time since he was a toddler.

Having been impressed by this new type of professional fighting, Amir looked up the cheapest MMA gym and signed up the next day.

[13] Amir's first fight came in the World Ultimate Full Contact 15, he submitted Pavlo Kulish in 59 seconds, and subsequently went on an 8 bout win streak to start his MMA career before moving to Bellator, where he extended that streak to 10 bouts after defeating Jamie Powell and Iurie Bejenari.

Amir's first loss came in the Middle Eastern promotion series Brave CF to Jose "Shorty" Torres.

[16] However, Paiva pulled out of the fight on 11 September citing a knee injury, resulting in Albazi's removal from the card.

[27] In late November, Royval pulled out of the bout due to a broken wrist,[28] and was replaced by promotional newcomer Alessandro Costa.

[35] It was reported that the bout between Albazi and Brandon Moreno was re-scheduled to take place on November 9, 2024 in the main event at UFC Fight Night 247.

[38] In an interview with BBC dated 16 December 2022, Albazi stated that he wants to become the first Arab UFC champion and plans to eventually return to Iraq and develop MMA there.