Anier joined Motherwell on loan from Viking FK last season and scored seven goals before signing for the club on a full-time basis last January.
The Estonian made 40 appearances for the Scottish Premiership runners-up and scored nine times during the 2013/14 season.
Anier told the club's website: “I had a big decision to make leaving Motherwell as it has been a brilliant place for me to play football.
"I really enjoyed things on and off the park. However, this was a good option for me and for the club, so it is one I had to take.
“I want to wish everyone at Motherwell the very best of luck for the future and thank everyone for all their support in the last year.”
Motherwell manager Stuart McCall said: “We have managed to keep the majority of our squad together this summer but when an offer comes along for a player, the club has to consider it.
“I’ve already been working on several options to replace Henri and now that his move is official, we will now look to pursue them.”