Madsen, who started wrestling at age of six, made his official debut at the 2008 Summer Olympics in Beijing, where he lost to Russia's Varteres Samurgashev in the first preliminary round of men's Greco-Roman 74 kg, with a technical score of 1–7, and a classification score of 1–3. At the 2012 Summer Olympics in London, England, Madsen was defeated by another Russian wrestler Roman Vlasov, in the second round of the men's Greco-Roman 74 kg category. Because his opponent advanced further until the final round, Madsen qualified for the repechage bout, where he scored four points and defeated France's Christophe Guénot. In the bronze medal match, Madsen was unable to score enough points in the first two periods, and lost to Lithuania's Aleksandr Kazakevič, finishing only in fifth position. Few months after the games, Madsen has signed a contract with European MMA, with sights on having his first fight inside the MMA cage by February 2013. In the 2016 Summer Olympics at Rio, Madsen won silver in men's Greco-Roman 75 kg, losing the final match against Roman Vlasov, who previously beat him in the 2012 Summer Olympics.
Madsen competed in two professional bouts in 2013 and 2014 but because he was receiving salary from the Danish Wrestling Federation for his commitment, Madsen was subsequently essentially forbidden to compete in mixed martial arts. Due to his retirement from wrestling, he was allowed to start training and competing in mixed martial arts. After amassing four straight professional victories in the regional circuit, Madsen signed with Cage Warriors. Madsen made his promotional debut against Alexandre Bordin at Cage Warriors Academy's inaugural event on September 23, 2018. The fight was largely contested on the ground, leading Madsen to a unanimous decision victory by dominant grappling. After the bout with Bordin, Madsen has been training at Xtreme Couture in Las Vegas. Madsen headlined Cage Warriors Academy Denmark2 against Mathew Bonner on December 15, 2018 and won the bout via unanimous decision. Madsen made his Cage Warriors debut against Thibaud Larchet at Cage Warriors 103 on March 9, 2019. Madsen won the fight via unanimous decision. Madsen faced Danish boxer Patrick Nielsen in an MMA bout at Olympian Fight Night1 on June 8, 2019. Madsen won the fight in the first round via rear-naked choke.
Ultimate Fighting Championship
As the first fight of his four-fight rookie contract, Madsen made his promotional debut against Danillo Belluardo on September 28, 2019 at UFC on ESPN+ 18. He won the fight via TKO in the first round. After recovering from shoulder injury and staph infection, Madsen returned to face Austin Hubbard March 7, 2020 at UFC 248. He used his superior wrestling to win the fight by unanimous decision despite suffering a broken jaw during the course of the bout.