The Brazil international was heavily linked with a return to the Premier League and reports have claimed that the midfielder preferred to return to Liverpool.
But Coutinho ended up joining Bayern on a season-long loan, while the German champions have the option to buy him from Barcelona for €120 million (£109.8m).
And Klopp was pleased to see his former player make the move to the Bundesliga.
He sent me a message and wished me luck, Coutinho told SportBild.
He said that Bayern are a big club and the Bundesliga a great league and that he is very happy to see me there.
Coutinho also praised Klopp for his management style at Liverpool.
Klopp is simply a great coach, one of the best in the world, a real leader, said Coutinho.