The 22-year-old has featured for the Scottish Premiership side in pre-season after a recommendation from compatriot and former 'Well player Henrik Ojamaa.
And he will go straight into the squad for Thursday's Europa League qualifier against Kuban Krasnodar.
Anier told the club website: "I'm really happy to join and I'm really looking forward to starting.
"My first impressions are really positive; the lads are really friendly and everyone from the manager to the rest of the staff are great so I'm really happy to be here.
"I want to keep working hard and do really well for the team and hopefully we can be successful this season.
"Henrik Ojamaa is my good friend and recommended me, telling me all positives about the club so I'm delighted to have joined Motherwell."