Wagner and his assistant Christoph Buhler have both been rewarded for guiding the Terriers to the Premier League with contracts that commit them to the club until 2019.
The permanent signing of Australia international Mooy, 26, was a key part of their plans for the top flight following last month’s dramatic Championship play-off final win over Reading.
Huddersfield have agreed to pay Manchester City an initial fee of £8m for Mooy, which is set to rise to £10m with add-ons.
The midfielder was Huddersfield’s player of the year last season as they secured a return to the top flight after a 45-year absence.
His arrival follows the signing of Belgian striker Laurent Depoitre, 28, from Porto for £3.5m.
Wagner has made a name for himself in England by transforming Huddersfield since leaving his job as Borussia Dortmund’s reserves coach to move to Yorkshire.
He was linked with Middlesbrough, Crystal Palace, Sunderland and Hull as he led the Terriers to promotion – while Wolfsburg were also keen to take him back to Germany last December.
The former United States international midfielder, born to an American father and a German mother, insisted last month that he was committed to the Terriers.
He said: “Come on, we have all been in this business for long enough to realise that if you are successful, they praise you, and if you aren’t successful, they kick you. This is nothing that bothers me.”
