"Under David's management, we took this club to the highest position it has held in nearly 50 years and created memories that will last forever", he said.
Wagner, whose final game was Saturday's goalless draw at Cardiff, departs after more than three years at the John Smith's Stadium.
Huddersfield were one of the favourites for relegation last season but Wagner kept them up with a 16th-place finish.
"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".
Hiring a new manager before the weekend's home clash with title-chasers Manchester City also looks ominous.
The 47-year-old held talks with the club's board this afternoon where a mutual decision was taken to terminate his contract. "Along with his family, he will always be a friend to me and Huddersfield Town".
Life has been tougher this season, Wagner's side undermined by a lack of a goalscorer and eight points from safety after only two wins from 22 games.
"There are four people in black and you have to ask them what was going on.I spoke to the linesman during the match and he said 'the first incident was not a foul and the second I don't know', but I don't know what he means".
Huddersfield chairman Dean Hoyle says he had "no intention of sacking David this season" but the coach "came to us and made it clear that he needs a break from the rigours of football management".
'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.
Wagner is now the fourth Premier League manager to leave their role this season, following Slavisa Jokanovic, Mark Hughes and Jose Mourinho. But Huddersfield have it tough with their next game against defending Premier League champions Manchester City. "Along with the technical staff, we'll give him all the support we can ahead of the game".