The Terriers, who sacked Simon Grayson three weeks ago after going 12 games without a win in the npower Championship, were granted permission to approach the 43-year-old on Tuesday after Coventry had rejected an initial approach.
Former Rotherham and Barnsley boss Robins, who had only been installed as Andy Thorn's permanent successor at Coventry in September when he signed a three-year contract, will take charge of his first game on Sunday when Town take on Wigan in the fifth round of the FA Cup.
Huddersfield chairman Dean Hoyle, who has handed Robins a rolling contract, said: "We've been through a lengthy and detailed process in appointing Mark as the club's new manager and we are delighted.
"As I said we would, we have taken our time in making this appointment because it is such an important one, both for our short and long-term ambitions.
"Obviously retention our Championship status is vital, but we also needed a manager who buys into the club's football philosophy and structure. We believe Mark is that man.
"Mark has the knowledge, skills and attributes that the board of directors set out for our new manager and it is clear that he shares our vision, philosophy and values."
- Sports & Recreation