The Frenchman and the Italian worked together at Juventus and Real, but will now be adversaries as coaches of two of the continent's top teams - starting on Wednesday
Ancelotti coached Zidane at Juventus and the Frenchman was his assistant when Madrid claimed their 10th European Cup crown by beating Atletico in Lisbon in 2014.
After a spell at Real's youth team, Castilla, Zidane is now in the top job at Madrid and led Los Blancos to another Champions League trophy with victory over Atleti again - this time on penalties - at San Siro in May.
But Ancelotti, now installed as Pep Guardiola's successor at Bayern, hopes his team will become the force in Europe in 2016-17.
"Zidane was my player, my assistant and I wish him all the best in Spain and a little less in Europe," the Italian said on Tuesday.
And he added: "Zizou was a great player and he has charisma. And that's very important to work with the players. He had everything needed to coach Madrid."
Previously colleagues at Juve and Real, Ancelotti and Zidane will now be rivals as coaches of two of Europe's elite teams and the two men meet as Bayern and Madrid square up in the International Champions Cup in New York on Wednesday.
Bayern lost on penalties to AC Milan after a 3-3 draw with the Rossoneri in their first ICC clash, before thrashing Inter 4-1 on Saturday.
Jerome Boateng has linked up with the Bayern squad after returning early from his holidays following Euro 2016. Meanwhile, Holger Badstuber has been training alone and Arjen Robben is back in Germany recovering from injury.
Xabi Alonso is fit and will face his former club, but a number of players (including Arturo Vidal, Thomas Muller, Kingsley Coman, Manuel Neuer and Robert Lewandowski) are still on holiday.
For Madrid, Cristiano Ronaldo and Gareth Bale are both unavailable, while Karim Benzema is stuggling to shake off a hip problem.
The Portuguese suffered a knee injury in the final of Euro 2016, with the Welshman still not back from his holidays after Wales made it to the last four in France.
Jese is on the verge of a move to Paris Saint-Germain and will not feature as Madrid step up their preparations for the UEFA Super Cup against Sevilla in Trondheim on August 9.
Zidane's men lost 3-1 to PSG in their first ICC fixture, before a 3-2 win over Chelsea on Saturday.
The transfer window has been quiet so far for Madrid, but Zidane said last week: "Anything could happen until the last day of the window."
Real kick off against Bayern on Wednesday night at 19:35 EDT (01:35 CET in the early hours of Thursday morning).