The 47-year-old, in charge at the John Smith’s Stadium since November 2015, departs with the Terriers sitting at the foot of the Premier League.
Huddersfield are eight points adrift of safety after a horrendous run that has seen Yorkshire’s sole top-flight representative lose eight of their last nine league games.
The Yorkshire Post understands the parting of the ways is on good terms with Wagner having approached the club over the weekend to suggest a change was needed.
He offered to remain in situ until the end of the season but, instead, a clean break has been made.
Wagner had two and a half years of a contract that was signed last summer to run but the past few weeks have taken their toll on a man who took Town into the top flight against all the odds and then kept them there at the end of last season.
Mark Hudson will take charge of Sunday’s home clash with champions Manchester City as the search begins for a new head coach.
Chairman Dean Hoyle said: “Under David’s management, we took this club to the highest position it has held in almost 50 years and created memories that will last forever.
“His achievements will rightly put him up there in Huddersfield Town history alongside great names like Herbert Chapman and Mick Buxton; legendary managers who changed the face of this club.
“As I had said previously, I had no intention of sacking David this season. Subsequently David – being the great man he is – came to us and made it clear that he needs a break from the rigours of football management.
“We discussed making that change immediately, but he also made it clear that he would give his all for the rest of this season before departing in the summer if we preferred.
“After a long discussion we all felt that David staying at the club until the end of the season was best, but we have kept discussions open and we all now feel that the time is right to part ways.
“I know the term ‘mutual consent’ is often a byword for the manager being sacked in professional football, but this is a truly joint decision.
“David has a real, genuine love for this club and, like me, his foremost concern in our talks has been to establish what is best for Huddersfield Town.
“I cannot thank David enough for what he has achieved. Along with his family, he will always be a friend to me and Huddersfield Town.”