The pair helped the Terriers secure Championship survival with a 2-1 win over West Bromwich Albion on Friday night, with only a mathematical miracle able to relegate the club to League One.
Cowley arrived at Huddersfield in September, with the side winless in their opening six league matches, drawing once while losing the other five.
Huddersfield Town Chairman Phil Hodgkinson thanked the pair for their efforts in helping the Terriers maintain their second-tier status but insists the decision was made in the best interests of the club in the long term.
“I would like to place my thanks on record to Danny and Nicky for their hard work and dedication towards securing the Club’s place in the Sky Bet Championship for next season," said
"That was the clear priority when they were appointed in September and we are very grateful that has been achieved.
“We all wish Danny and Nicky all the best for the future and they leave with my best wishes in their future endeavours.
“However, we have made this decision in the belief that, in the long term, it is in the best interests of the club as we move forward.
"We have a different vision for the way we operate the club, and how our ambitions can be achieved.”
In a statement, the club said they are not "seeking applications for the vacant position".