The Italian on Monday signed a three-year contract with the Turkish champions, who parted company with Fatih Terim last week.
Mancini had been out of a job since being dismissed by Manchester City in May.
"I am very happy to have arrived to a great club like Galatasaray," Mancini said. "This is a beautiful and interesting challenge and I believe I have made the right choice.
"Wednesday's game against Juve will be very important and for me this is a happy coincidence."
This is not the first time Mancini has come up against Juve in continental competition.
While in charge of City, he faced the Turin club in the 2010-11 campaign in the Europa League, with both games finishing in 1-1 draws.
Galatasaray travel to the Juventus stadium on the back of Saturday's 1-1 result against Caykur Rizespor.
The outcome left Gala in 10th position in the Turkish Super League, eight points behind leaders Fenerbahce but having a game in hand.
Gala are hoping to make amends for their dismal showing in their 6-0 home defeat to Real Madrid in their Champions League Group B opener.
That reverse stunned many, including Juventus coach Antonio Conte.
"When I saw the result, I thought something seemed a bit strange so I watched the game and realised it was not a fair score," he said. "It was too harsh on Galatasaray.
"We know that it won't be easy because Galatasaray have some top players.
"(Didier) Drogba is great on the field, a leader and an example."
Conte has great respect for compatriot Mancini, who led Inter Milan to three Serie A titles.
"It's a pleasure to come up against Mancini," he said. "He's won in Italy and he's won abroad.
"I rate him as one of the best coaches in Europe and it's only right that he's back in the game, and Galatasaray have strengthened further with his arrival.
"I would have preferred not to have met him tomorrow because when a club changes coach, it becomes hard to study how to face up to them.
"I don't think Mancini can transform things in a day, but it's for this reason that I would have preferred to face Galatasaray when I already knew how they would play."
Juve also endured a disappointing start to the competition with a 1-1 draw at Copenhagen.
The Italian champions head into the contest on the back of last weekend's 1-0 triumph over city rivals Torino.
Juve are unbeaten and lie second in Serie A, two points adrift of Roma.
Juve striker Carlos Tevez, who played under Mancini at City, has failed to recover from a left ankle wound sustained on Saturday and will not feature.
The visitors are without midfielder Wesley Sneijder, who is out with a muscular injury.
However, Drogba has shaken off a muscular problem and will lead Galatasaray's attack.