After weeks of speculation, Huetter, 51, will sign a three-year contract as head coach of Gladbach, replacing Marco Rose, 44, who is leaving to take over at Borussia Dortmund for the 2021/22 season.
With six games left, fourth-placed Frankfurt are on the verge of qualifying for the Champions League next season. They have a five-point lead over fifth-placed Dortmund.
In contrast, Gladbach are eighth in Germany's top flight, 13 points from a place in the Champions League.
By coincidence, Borussia Moenchengladbach host Eintracht Frankfurt in the Bundesliga on Saturday.
Huetter informed Eintracht's bosses on Monday, and the team on Tuesday morning, that he is leaving due to a release clause in his contract.