Both players have penned five-year deals with the Bavarian club.
"Michael Gregoritsch is a young player, who scores goals, has experience of the Bundesliga and can play across the attack," said Augsburg sporting director Stefan Retuers. "We're delighted he's chosen to join FCA."
Twenty-two-year-old Gregoritsch, who scored ten goals in 55 top-flight outings for HSV, is in little doubt he has made the right choice.
"I have the feeling that FCA are exactly the right club for me," the Austria international midfielder explained. "Everything suits me here, that's why I'm tied to a long-term deal. I'd like to help further Augsburg's fantastic progress in the years ahead."
Watch: Michael Gregortisch passes his Augsburg audition with flying colours
While Gregoritsch is a familiar face to Bundesliga audiences, 19-year-old Cordova is something of an unknown quantity - although he did score four goals at this summer's FIFA U-20 World Cup for beaten finalists Venezuela.
"In Sergio Cordova, FCA have acquired a young talent who made a real impression at the U-20 World Cup," said Reuter. "We're convinced he'll deliver in the Bundesliga and we will give him the necessary time to acclimatise and develop."
Cordova, for one, cannot wait to get started. "The Bundesliga is a big challenge for me, and I'm very grateful to the club for putting their faith in me and giving me the opportunity to take this step. I want to settle quickly and develop, so that I can help the team reach their objectives."