Anier, whose loan spell was set to expire next week, has signed a two-and-a-half-year contract.
The 23-year old has scored seven goals and formed a prolific partnership with John Sutton.
Anier told MFC TV: "I am really happy things are tied up and my long-term future is sorted out.
"I've really enjoyed the last six months in Scotland, the physicality of the game and how high-tempo it is.
"It's quick and technically good too, a real challenge.
"It is important for any footballer to feel happy and welcome and the club, on and off the park, has did that for me and made it easy.
"I enjoy working under a great manager and coaching staff and training with the lads.
"It's also a pleasure to play in front of the fans, who have been so good with me.
"My aim now is to try and develop as a player, score as many goals as I can for Motherwell and hopefully finish as high up the table as possible.
"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."
The deal was made possible partly because Motherwell have loaned defender Adam Cummins to Dundee, with another player set to move on loan next week.
And Anier's wages until the end of this season will also be paid from directors' loans.
Chief executive Leeann Dempster urged fans to respond to the news by joining the Well Society, which has been set up to provide community ownership of the club.
She 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.
"It does not take an accountant to realise the impact of being knocked out of both cup competitions for a club like ours.
"It has been a great few weeks on the park, however, somewhat more financially difficult off it.
"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.
"It is more important than ever that we all show our passion and dedication by supporting the club as much is possible. To do this, I would urge anyone considering joining the Well Society to do so.
"The society is key to the success and future of the club. There has been somewhat of a lull in new memberships recently. Signing both players gives us all the chance to refocus and start these important discussions once again."