"I'm very excited to be playing the Laver Cup in September," Fognini said in a statement. "Playing as part of a team is special in tennis, where we are more used to having a one-on-one battle every match.
"I'm looking forward to competing alongside all the great players on Team Europe."
Federer, one of the instigators of the team event that will have the full backing of the ATP Tour this year for the first time, and Zverev have been ever-presents while Spaniard Nadal missed last year because of injury.
Thiem, runner-up to Nadal at the French Open on Sunday for the second year in a row, missed out last year but Swedish great Borg is happy to have him back.
"I'm delighted to have Dom (Thiem) back in the team. He was a great player for us in Prague and his form is outstanding, as we saw recently at Roland Garros," Borg said.
Borg still has one spot to fill for the three-day match.
Team World Captain John McEnroe will announce his first team members in the coming weeks.
(Reporting by Martyn Herman; Editing by Alison Williams)
