The deal brings to an end Newcastle's long-term pursuit of the 24-year-old, who becomes their fourth signing of the transfer window following the arrivals of Ayoze Perez, Jack Colback and Siem de Jong.
Newcastle appeared to have recruited Cabella in January, only for the deal to fall through.
However, Montpellier chief executive Laurent Nicollin confirmed on Friday that an agreement had been reached between the clubs.
The fee paid for the France international has not been disclosed, although it is believed to be in the region of £12 million.
"It is great to finally be a Newcastle player," Cabella told the Premier League side's official website.
"This is a move that I really wanted to make, as I have heard nothing but good things about Newcastle United from everyone I spoke to.
"I wanted to join a great English club and that is why I have arrived here. I'm looking forward to pulling on the shirt and playing in this magnificent stadium, and I will give this club my maximum."
Cabella has long been regarded as one of the most exciting young players in France, and was called into his country's FIFA World Cup squad following injuries to Franck Ribery and Clement Grenier.
The Corsican-born playmaker did not make an appearance for Didier Deschamps' men in Brazil, but his stock has risen significantly in recent times after a strong 2013-14 campaign.
A Ligue 1 title winner with Montpellier in 2011-12, Cabella scored 14 goals for Rolland Courbis' side last term.
Newcastle manager Alan Pardew added: "Remy is a player who has been on our radar for a while and we are delighted to bring him to the club.
"He is a player who I am sure will excite our fans. He has flair, hard work and commitment, and is going to bring a talent, energy and quality to St. James' Park that our supporters will enjoy.
"Remy has great ideas when the ball comes to him, and along with Siem de Jong is going to improve an area where we definitely needed some help."
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