The 22-year-old joins for an undisclosed fee, reported to be £11.44m (13m euros) plus add-ons.
The Benin international, who scored 14 goals in 32 starts for Montpellier last season, has signed a four-year deal.
The Terriers have also signed full-back Scott Malone from Championship side Fulham on a three-year deal for an undisclosed fee.
Huddersfield have broken their transfer record three times in a fortnight. Porto striker Laurent Depoitre joined for £3.5m on 23 June before Manchester City midfielder Aaron Mooy was signed for an initial £8m last week.
Huddersfield head coach David Wagner said: "Steve has real physical attributes that should be perfect for the Premier League.
"We have met and I know he is a great character," Wagner added. "At just 22 years old, he is only going to improve too. Given what he is already capable of, that is very exciting."
Mounie has been capped seven times by Benin, but does not require a work permit as he has dual French nationality.
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Huddersfield Town have signed striker Steve Mounie from Montpellier for a club record fee.