The Estonia striker - on loan at the club since the summer - joins from Norwegian club Viking Stavanger on a two-and-a-half-year deal.
Anier's seven goals this season have helped maintain Motherwell's push for a second straight top-two finish.
And he told the club's official website: "I am really happy things are tied up and my long-term future is sorted out.
"I really enjoy it in Scotland, the physicality of the game and how high-tempo it is. It's quick and technically good too, a real challenge.
"My aim now is to try and score as many goals as I can for Motherwell and hopefully finish as high up the table as possible.
"I loved playing in the Europa League last year, although it was a difficult game in Russia, and I would certainly like another shot at it again. To do that, the team is going to push as hard as we can and that's our aim."
The deal for Anier comes a week after 'Well struck a deal to keep Lionel Ainsworth on loan until the summer.
Chief executive Leeann Dempster said: "As a board we have worked incredibly hard to keep both Lionel Ainsworth and Henri Anier at Fir Park against what is a tough financial climate within the game.
"I want to pay special tribute to two directors in particular who helped fund the Anier deal; it would not have been possible otherwise.
"This gesture shows that we have a special bond at our club, with great people who all pull together. That includes the staff, players, directors and fans."