Robins took the reigns at Coventry last September and has since lifted the Sky Blues from the League One relegation zone to eighth place in the table.
Coventry granted Huddersfield permission to talk to Robins about their vacant managerial post earlier this week despite rejecting an initial approach.
Huddersfield have been without a manager since Simon Grayson was sacked in January.
Terriers chairman Dean Hoyle 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 of 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.
"He has good knowledge of the division from his previous spell with Barnsley.
"He has also shown an ability to develop young players. Indeed, his work with the FA on the Elite Player Performance Plan and his commitment to development was a big factor in his appointment.
"Mark has shown his skill in getting the most from the resources at his disposal, none more so than his recent achievements at Coventry."
The former Rotherham and Barnsley boss will take charge of his first game on Sunday when Huddersfield take on Wigan in the fifth round of the FA Cup.
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