Coutinho traded Barcelona for Bayern in a season-long loan deal.
The Brazilian was no longer wanted in Catalonia after the arrival of Antoine Griezmann.
And Klopp thinks his former player will enjoy the Bundesliga.
He told Kicker: "Coutinho didn't get to play in his preferred No 10 role all that much when he was with us, but he's a great No 8 and is a fantastic left-winger because he's incredibly good in tight spaces and has the pace to exploit bigger spaces.
"He dominates football matches, and is a real asset if he can put his stamp on the team.
"Bayern needed him, and Bayern wanted him. If they can integrate him and get the very best out of him, the Bundesliga will have a top player on its hands.
"Coutinho has an unbelievable eye for goal from range.
"I haven't seen a player coming in off the left and striking the ball with such regularity and precision from those kind of positions since (Alessandro) Del Piero."