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.
Mounie scored 14 goals in 32 Ligue 1 appearances last season, placing him among the top 10 scorers in France, and did not need a work permit due to his dual French nationality.
A deal had been agreed and the striker passed his medical a few days ago, but the announcement was delayed because of the passing of Montpellier’s president Louis Nicollin. His funeral took place on Tuesday.
Huddersfield head coach David Wagner told the club’s website: “I’m delighted that we could sign Steve ahead of the start of pre-season training.
“He has a very exciting combination of attributes that makes his a very attractive proposition as a young striker.
“He has real physical attributes that should be perfect for the Premier League, plus we have already seen his talents as a football in his remarkable season in France.
“We have met and I know he is a great character. For a man of his young age, he already has great experience both in life and as a footballer from his time in France, playing in a high-quality Ligue 1.
“At just 22 years old, he is only going to improve too. Given what he is already capable of, that is very exciting.”
Huddersfield have broken their transfer record three times in a fortnight. Porto striker Laurent Depoitrejoined for £3.5m on 23 June before Manchester City midfielder Aaron Mooywas signed for an initial £8m last week.