The final three teams were added to the field on Thursday.
The Romanian hopes to pick up confidence to take into the 2022 season.
The Scot knows his time is coming, even if things haven't clicked as fast as he'd like.
The Italian is the sixth ATP singles player to qualify, leaving two spots up for grabs.
The trio are the fifth, sixth and seventh players to qualify for the WTA Finals.
The top two players have signed on for this year's 18-team Davis Cup Finals
The Davis Cup Finals are set for November 25-December 5th in Turin, Italy, and Madrid, Spain.
