Gladbach sacked Eugen Polanski on September 13th and brought in Jan-Moritz Lichte on an interim basis, but it did not improve their fortunes as they lost 4-3 to Mainz the following weekend.
Blessin has a contract until June 2028.
His last job was a two-year spell at St Pauli that ended in June, having taken over after they were promoted to the Bundesliga under Fabian Hurzeler and kept the club in the top flight for a season before they were relegated last term.
"Blessin will be officially unveiled at a press conference at ista-Borussia-Park at 13:30 CEST on Wednesday, 23rd September, with Head of Sports Rouven Schroeder in attendance," said Gladbach in a statement on their website.
The St Pauli job was Blessin's first as a senior manager in German football, although he spent eight years at RB Leipzig as a youth coach after being brought in by Ralf Rangnick.
Previously, he had spells in Belgium and Italy, taking charge of KV Oostende, Genoa and Union Saint-Gilloise.
Gladbach finished 12th last season, nine points clear of the relegation playoff position. Blessin will have time during the international break to work with his players before they return to action in the Bundesliga on October 11th at FC Koln.