Djokovic's win gave Serbia an unassailable 2-0 lead ahead of the doubles to set up a meeting with either the Nick Kyrgios-led Australia or Rafael Nadal's Davis Cup champions Spain in the final.
Novak Djokovic and Rafael Nadal urged organisers of the ATP Cup and Davis Cup Finals to consider a possible merger, saying it makes little sense to have two men’s team competitions on the tennis calendar.
After a 7-5, 7-5 defeat to Dominic Thiem in his tournament opener, six-time champion Roger Federer may find it tricky to qualify for the last four of the ATP Finals.
The 32-year-old Serbian tennis star avenged his loss to the 21-year-old Greek 3 weeks earlier in the Shanghai Masters, with a 58-minute victory.
Meanwhile, world number one Novak Djokovic defeated Britain’s Kyle Edmund with 7-6(7) 6-1 to reach the Paris Masters quarter finals.
Former world number one Murray, who appeared on the brink of retirement after losing in the first round of the Australian Open in January, battled back from a set and a break down to win the European Open 3-6 6-4 6-4.
US Open runner-up Medvedev, chasing his fourth ATP Tour title in a breakthrough 2019 season, will meet Germany's Alexander Zverev in Sunday's final.
Grigor Dimitrov, 78th-ranked, delivered a stunning upset of Roger Federer in the US Open quarter-finals, fighting back for a 3-6, 6-4, 3-6, 6-4, 6-2 triumph over the Swiss star who had beaten him in all seven of their prior meetings.
Champion Novak Djokovic elected to retire in the third set due to a left shoulder injury. He was facing off Stan Wawrinka who was leading 6-4, 7-5, 2-1.
Federer, a seven-time champion, was ousted from one of his favourite tournaments in barely over an hour, falling in straight sets to a 21-year-old Andrey Rublev he had never faced.
Never before has a final in London lasted so long - it went into the twelfth game of the fifth set and then into the tiebreak.
The most captivating modern rivalry in men's tennis returns to the scene of its most dramatic episode when Roger Federer and Rafael Nadal meet for a place in the Wimbledon final.
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