The 22-year-old Benin international, who has dual French nationality, scored 14 goals in Ligue 1 last season.
Town boss David Wagner told the club's official 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 him a very attractive proposition as a young striker."
Town have repeatedly broken their club record fee this summer, first with the reported £3.5m signing of Belgian striker Laurent Depoitre from Porto and then in turning midfielder Aaron Mooy's season-long loan from Manchester City into a permanent deal for £8million, rising to £10m with add-ons.
The fee for the 6ft 3in Mounie has been reported as £11.5m and Wagner said: "He has real physical attributes that should be perfect for the Premier League, plus we have already seen his talents as a footballer 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."
Mounie said he had fulfilled a lifelong dream with a move to English football.
"It is a big challenge for me and I hope I will do very well," he told HTTV.
"We know how the Premier League is the best championship in the world and it was a dream when I was young and it was a goal for me.
"Now I am here and I will work very hard to do my bit for the team."