Schalke announced Wagner's hiring last week with the former Huddersfield Town manager signing a three-year contract to join the German side.
Wagner, who will take over from interim coach Huub Stevens, has long been one of Klopp's closest friends since the two were team-mates at Mainz throughout the 90s, and was best man at the Liverpool manager's wedding in 2005.
Klopp had Wagner on his staff at Borussia Dortmund until the Liverpool boss' departure in 2015 with his former assistant soon moving to take over Huddersfield Town.
And, with Wagner now set to take over at Schalke, Klopp says the club clearly made a good decision in hiring his long-time friend.
"I can only congratulate Schalke, even if my Dortmund friends do not like to hear that," the former Dortmund said coach in an interview with SPORT1.
He also had a stint with Schalke from 1995-97, going on to make 29 appearances and scoring two goals for the club.
Internationally, he represented Germany at a youth level before making the switch to join the U.S. national team, earning eight caps.
With Schalke, Wagner will now manage several American prospects, including Weston McKennie, Nick Taitague and Haji Wright.
During his time at Huddersfield, Wagner guided the club from the Championship to the Premier League via the play-offs in 2017.
The club survived its first season in the Premier League, defying the odds to finish 16th in the league.
But the 2018-19 season proved too much for the club, with Wagner leaving the club by mutual consent in January as the Terriers finished last in the league with just 16 points.
His new club, Schalke, have struggled this season as well, currently sitting 15th in the league with one match to play.