The five-year deal sees Die Blau-Weißen fend off rumoured interest from clubs such as Arsenal and Borussia Mönchengladbach to secure the player's signature, after Duda impressed in his three appearances for Slovakia during Euro 2016.
Speaking to the club's official website, head coach Pal Dardai said he is "very excited" to have signed "a young, exciting player with lots of potential", adding that despite the player's age he has "already collected a lot of experience."
Duda was included in the Slovakian squad ahead of Euro 2016, and scored in their 2-1 defeat to eventual semi-finalists Wales, before he and his team-mates were knocked out of the competition thanks to a 3-0 loss to Germany in the round of 16.
The 21-year-old was also a regular starter in Legia Warsaw's title winning campaign last season, making 27 appearances and scoring two goals as well as appearing 11 times in the UEFA Europa League for the club, where he again found the net twice.
No European involvement for Duda
Unfortunately for Hertha however, Duda was one of the players that featured in Legia Warsaw's Champions League qualifier against Zrinjski Mostar last Tuesday meaning he will be unable to participate in any Europa League qualifiers for his new side, who finished 7th in the Bundesliga last season.
The Slovakian will however be eligible to play when Hertha begin the 2016/17 Bundesliga campaign at home to newly promoted SC Freiburg, who won the 2. Bundesliga title in the 2015/16 season.
Although Duda is the club's first purchase in the summer window, Hertha have moved several players on, with Roy Beerens the only permanent departure after he joined Championship side Reading in a deal worth €1m.
The other departures include goalkeeper Sascha Burchert and full-back Johannes van den Bergh, who moved on after seeing their contracts at the club expire, whereas goalkeeper Marius Gersbeck signed for third division outfit VfL Osnabrück on loan until the end of the season.