Covic, who had two spells at Hertha as a player, currently coaches the club's Under-23 side and will step up to succeed Dardai for the 2019-20 season.
Former Hungarian footballer of the year Dardai has been in charge for four-and-a-half years but his departure from the club was announced last month.
In the wake of the announcement, Covic spoke to the club's official website about his new role.
"For me as someone who was born in Berlin, played for Hertha and worked for the club for years, it is like a dream come true,” the 43-year-old said.
“Hertha has never just been a normal employer for me – this club is my passion and has a place in my heart.
“I will bring this passion and emotion into the team. That's only possible together. I am a team player who is very approachable and I value hard work. That is the only way you can fuel enthusiasm and keep developing.
“I was able to experience the Hertha fans as a player and I'm really looking forward to doing it again as the coach. My excitement couldn't be greater.”
Covic's former team-mate Mirko Dickhaut will join him on the backroom staff, with goalkeeping coach Zsolt Petry and fitness coaches Henrik Kuchno and Henrik Vieth retained.
Hertha's last Bundesliga game with Dardai in charge is at home to Bayer Leverkusen next Saturday. They sit 10th in the table.