Jeong started his career with Jeju United.[3] Jeong Taewook then transferred into Daegu FC after spending a year with Jeju United After a successful run at Daegu FC for 4 years, Jeong was sold to Jeonbuk Hyundai Motors in January 2023. Jeong has since had 39 appearances and 1 goal for the club
Jeong made his international debut during the 2017 FIFA U-20 World Cup held in South Korea.
Jeong was then selected to represent South Korea for the 2018 Asian Games. South Korea had emerged as champions in the 2018 Asian Games after beating arch-rivals Japan 2-1 in extra time during the finals winning them the gold medal.
Jeong was also named in the AFC U-23 Championship Thailand 2020 squad. South Korea had won the championship after beating Saudi Arabia in the finals. Jeong was named Man Of the Match after scoring the winning goal during the finals. He was selected as the Best 11 for the tournament.
In 2021, Jeong Taewook was named in the 22-man squad for the 2020 Tokyo Olympics. Jeong Taewook was selected as captain for the tournament and help led the team to the quarter finals of the competition. However South Korea's journey ended there as they had lost 6-3 to Mexico.