Turin, Innsbruck and Madrid are the venues, with the Spanish capital hosting the last five days as part of the final year of its staging agreement.
The ITF and Kosmos – which was founded by Barcelona footballer Gerard Pique – announced a 25-year, $3bn (£2.25bn) partnership in 2018.
It spelt the end of the traditional format of home and away ties spanning a whole year, and led to the creation of an 18-team Finals.
Spain were the inaugural winners of that event, in Madrid two years ago.
There is $20m (£15m) of prize money for the players at this year’s Finals, as well as the substantial fee Kosmos pays to the ITF for the development of tennis around the world.
But with Kosmos believed to have lost tens of millions of dollars on the 2019 event, something had to change.
The fee it receives from Abu Dhabi will significantly ease its financial burden, but the competition will become less attractive if more of the top players stay away.
Seven of the world’s top 20 are competing in this year’s Finals, including the top two of Novak Djokovic and Daniil Medvedev. World number three Alex Zverev is the most high-profile player to have opted out, but others have withdrawn because of injury and fatigue.
The other major concern will be the spectators, or lack of.
The Abu Dhabi Formula 1 Grand Prix has attracted reasonable crowds over the past dozen years, but international cricket in the region has been poorly attended, and the stands for the 2019 World Athletics Championships in nearby Doha were virtually empty.
Partisan fans have made the atmosphere at many past Davis Cup ties very special, but given the cost of flights and accommodation in Abu Dhabi, it seems the Finals will attract even fewer travelling supporters in future.
A five-year run in Abu Dhabi would at least offer the competition some stability, and it is possible the ATP Cup will be subsumed into the Davis Cup by the end of the deal.
Conversations between the ITF and the ATP have been more productive in recent months, as the two organisations consider combining their team events.
But as things stand, and for another couple of years at least, the ATP Cup will take place in Australia only four weeks after the Davis Cup Finals draw to a close.