Shrimpers academy graduate Payne, 21, scored 17 goals in 88 games for the club, having made his professional debut in August 2013.
The League One side will be owed a compensation fee.
"In my opinion he is probably one of the most interesting young British midfielders in the country," Terriers head coach David Wagner said.
"Jack is already excellent technically and has a great record of scoring goals, but at just 21 he has lots of room to develop further.
"His desire to improve was very clear from our very first meeting and he will do that with us in the Championship."
Huddersfield finished 19th in the Championship table last season, 11 points clear of the relegation zone.
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Championship side Huddersfield have signed midfielder Jack Payne after he rejected a new contract at Southend.