ATP World Team Cup: New 24-team tournament to launch in 2020
A revamped World Team Cup will take place in Australia in the first week of January from 2020, the ATP said.
It comes after the International Tennis Federation set out plans for a rival 18-team end-of-season event to crown the Davis Cup champions from 2019.
In May, ATP executive chairman Chris Kermode said staging both tournaments within six weeks would be "insane".
But on Sunday he said: "This announcement will change the landscape of the ATP World Tour."
He added: "We believe this outcome will deliver long-term sustainability not only financially but also from a player health perspective, which is critical. This event has huge potential and we now look forward to working together with Tennis Australia in bringing our vision to fruition."
The ITF responded to the announcement by saying it was an "opportunity missed".
"Today's news that the ATP board has decided to proceed with the World Team Cup does not change the commitment of the ITF to proceed with a new Davis Cup event in 2019," the ITF said. "We do feel that this was an opportunity missed by the ATP to work together with the ITF in a beneficial and positive way for the whole of tennis.
"Our plan is transformative. It includes format changes to Davis Cup that were requested by the ATP Player Council in 2016 and it will create a world class finale to the tennis season."
The World Team Cup will take place in partnership with Tennis Australia and will feature 24 teams, offering £11.35m in prize money. Ranking points will also be available.
The tournament had previously taken place in Dusseldorf from 1978 to 2012.
Federations will vote at the ITF AGM in August on proposals to transform the Davis Cup, culminating in an 18-nation World Cup-style tournament at the end of the season in November.
The ATP and ITF had been in discussions to try to resolve the issue.
Russell Fuller, BBC tennis correspondent
"Hopefully tennis works together and we come up with a solution," Chris Kermode said in May.
Well, tennis tried to work together but ultimately the ATP Board has voted in favour of staging its own event. This leaves us the ludicrous prospect of having an ITF World Cup and an ATP World Cup within the space of six weeks.
The ITF's next task is to secure a two-thirds majority vote in favour of a reformed Davis Cup at next month's AGM. It must then persuade a substantial number of the world's top 100 to play in an event which is likely to be very lucrative, but will reduce the off season to a mere five weeks.
The ATP's challenge, meanwhile, will be to turn a revamped World Team Cup into an event worthy of the name, and not just an opportunity for a glamorous tune up before the Australian Open.