(BBC): The Russian dug deep to claim a 4-6 7-6 (7-2) 6-4 victory over world number three Thiem at the O2 Arena.
Thiem led the second-set tie-break but Medvedev reeled off seven points in a row to force a decider and came through a tight final set to ensure victory.
The 24-year-old will finish the year fourth in the world rankings.
Medvedev is the only player to beat the three highest-ranked players at the season-ending event, following his earlier victories over Novak Djokovic and Rafael Nadal.
He did not beat a single top-10 player from November 2019 to October 2020 but has now beaten seven in the space of four weeks.
It was the last year the tournament was being held in London, with the event moving to Turin, Italy, from 2021.
With no crowd in the stadium because of coronavirus restrictions, Medvedev’s celebrations were muted before he and Thiem had a lengthy hug at the net.
Despite the loss, Thiem can still reflect on a solid year in which he has reached two Slam finals, losing to Djokovic at the Australian Open before claiming his maiden major title in New York.
Medvedev, who went unbeaten in the group stages, is credited as one of the men’s tour’s quickest problem solvers.
A gangly player who has been jokingly nicknamed ‘the machine’ by his competitors, he is capable of changing the direction of rallies with ease and his own forehand – while flatter than Thiem’s – is equally effective.
His repeated moves to the net as the match progressed allowed him to hurry through his service games and surprise Thiem with a change of pace.
However, the Russian let the opening set slip. Having been in control in the early stages and racing to 40-0 on his own serve, Medvedev lost four points through a series of sloppy forehand errors before double-faulting to hand Thiem a crucial break.
His recovery in the second-set tie-break changed the tone of the match and Medvedev gritted his way through a tough fifth game in the third set, converting his ninth break point to take the crucial lead.
He was the stronger of the two players as the match progressed, drawing more errors out of a tiring Thiem’s backhand, and he claimed victory when Thiem sent a return of serve into the net.While there will be obvious disappointment for Thiem in losing in the final for a second consecutive year, the 27-year-old has improved his all-round game in another solid year.
Once thought of as a solely clay-court player, Thiem’s biggest career title came on a hard court, and he too beat Djokovic and Nadal in London to progress to the final.
Thiem prospers through his big groundstrokes and an increased confidence in his serve. With Medvedev having the better of the longer rallies, Thiem kept the points short, using his slice to stop Medvedev unleashing his own heavy shots.
He staved off two break points in his opening service game, finding an inside-out forehand and an ace at the key moments in a 10-minute game.
When Medvedev’s level dipped in the next game, all Thiem had to do was get the ball back into play, capitalising on his opponent’s mistakes before rushing through a tidy service game of his own.
He took the first set in fortunate style, a net-cord winner almost hitting Medvedev, but both players smiled and laughed at the changeover before resetting for the second.
Thiem had a chance to take the second set, racking up two break points in the seventh game thanks to his deep hitting. However, Medvedev was able to find his first serve when he needed it most, and that missed chance led to the tie-break that the Russian ran away with.
Thiem reeled off five straight points to overturn a 0-40 deficit early in the third set but the Austrian grew more frustrated as he was outwitted by Medvedev.
Earlier, Wesley Koolhof and Nikola Mektic won their first doubles title together with a 6-2 3-6 10-5 victory over Jurgen Melzer and Edouard Roger-Vasselin.