David and his older brother Daniel started out doing Muay Thai as youths, David started in 2004 at the age of 15, they had grown up watching their older brother Gabriel competing in kickboxing and boxing. David had a decorated amateur career, at the highest point when he won a bronze medal at the IFMA World Championship A-class in Bangkok, Thailand in 2009. He also won the Nordic Championship once and the Swedish national Championship three times. He also competed professionally, where he completed a record of 39–2, with 11 wins by KO/TKO. He won the 2011 King of the Ring tournament in Oldenzaal, the Netherlands.
Still competing in kickboxing and muay thai at the time, David and his brother Daniel Teymur started to train MMA in 2012–2013. David made his MMA debut on October 19, 2013 at International Ring Fight Arena 5, where he lost by decision against Mattias Rosenlind. He rebounded from the loss as he had his next two fights in the same promotion, defeating Veselin Dukov by unanimous decision on April 5, 2014 and on November 22, 2014 he defeated Gaik Pogosyan by a first-round TKO due to knees. On April 4, 2015 he fought Robin Tuomi at Trophy MMA 6. Teymur won the fight by TKO due to leg kicks and punches in the first round.
''The Ultimate Fighter''
In August, 2015 it was announced that Teymur was selected for. To get into the TUF house, he defeated Thibault Gouti by unanimous decision. In the elimination round he fought Johnny Nuñez. Teymur dropped Nunez with knees to the body early and with a left hook late in the fight. He won the fight by unanimous decision. In the quarter finals he fought Marcin Wrzosek. He lost by majority decision.
Teymur made his UFC debut against TUF teammate and fellow Swedish fighter Martin Svensson on February 27, 2016 at UFC Fight Night 84. He won the fight by TKO after he knocked Svensson down with an uppercut in the second round. His next fight was against Jason Novelli on August 6, 2016 at UFC Fight Night 92. Teymur scored a knockdown from a straight left hand in round 1. In round 2 he scored two knockdowns, first by another straight left and moments later he won the fight by knockout after dropping Novelli to the canvas by a right-left hook combination. In his third fight with the promotion Teymur took on highly touted Lando Vannata on March 4, 2017 in the co-main event at UFC 209. Despite coming in as a 3-1 underdog, Teymur got the upset and won the fight by unanimous decision. The fight was awarded Fight of the Night honors. Teymur next fought undefeated Drakkar Klose on December 2, 2017 at UFC 218. He won the fight by unanimous decision. Teymur was expected to face promotional newcomer Don Madge on May 27, 2018 at UFC Fight Night 130. However, Madge pulled out of the fight in late April with an undisclosed injury. As a result, Teymur was removed from the card entirely and rescheduled to face Nik Lentz the following week at UFC Fight Night 131. He won the fight by unanimous decision. Teymur faced Charles Oliveira on February 2, 2019 at UFC Fight Night 144. He lost the fight via an anaconda choke submission in the second round.
Personal life
Teymur's older brother, Daniel Teymur, is also a MMA fighter and currently signed with the UFC. Both brothers transitioned to MMA from kickboxing and Muay Thai in 2012, making their debuts in 2013. A few years later both got into the UFC. David was signed in 2015 and Daniel in 2017. He is of Syrian descent.