The announcement of the 24-team event comes three months after the International Tennis Federation - backed by a group of investors spearheaded by Barcelona soccer player Gerard Pique - said it would hold a one-week competition for 18 nations in Madrid in November 2019.
Federer was upbeat about the new event and said the Davis Cup would not suffer.
In May, ATP executive chairman Chris Kermode said staging both tournaments within six weeks would be "insane".
World number 1 and the five-time ATP Finals champion Novak Djokovic has played another impressive match to leave Guga Kuerten Group with a flawless 3-0 score, ousting Marin Cilic 7-6 6-2 in an hour and 33 minutes for his 34th win at this tournament overall and the 52nd in 2018 so far and the 46th in the last 51 matches after Madrid! "I'm really, really confident that down the line we will find a resolution for this".
Ranking points will be on offer along with an £11.35m prize pot, with qualification based on the ranking of the country's No 1 player.
The ATP Cup, announced by the ATP and Tennis Australia on Thursday during the ATP Finals in London, will be played from 2020 across three Australian cities over 10 days in the lead-up to the Australian Open, the first Grand Slam of the year, which starts in January.
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"This event will help us all achieve that while connecting with new generations of tennis fans".
"I like that it's owned by ATP, by the players, and that we have ranking points, and it's going to be the best way to kickstart the season", said world number one Djokovic. This was their 19th meeting and the 17th win for the Serb who wasted a match point against Marin in the final at Queen's in June before beating him in Cincinnati, Paris and here in London.
The Davis Cup is run by the ITF, the governing body of world tennis, while the ATP, which runs the men's Tour, will stage the ATP Cup.
"We have Davis Cup, obviously, that has been the most historical team event", said top-ranked Novak Djokovic, the president of the ATP Player Council.
"More than 90 percent of the time we're playing as individuals and we don't have too many team events". You would think the players are going to play that. "It will happen that we will have two average events".