Davies, who earned his maiden international cap against Tonga in June, started Wales' 24-22 win over South Africa in Cardiff on Saturday.
He has signed a two-year deal at the Liberty Stadium and follows in the footsteps of international team-mate Scott Williams, who will also swap the Scarlets for the Ospreys, it was confirmed last week.
"It's been an incredibly hard decision to leave my boyhood club at the Scarlets where I've had a fantastic nine years at the club and leave many good friends," Davies said.
"However, having sat down a few times with [Ospreys head coach] Steve Tandy, it was clear that moving to the Ospreys was the correct rugby move for me and will allow me to develop further as a player.
"I believe the Ospreys game plan will suit my style of play and I'm very excited about trying to form a good partnership with Sam Davies, hopefully playing a big part in future success at the Ospreys.
"For now though, my focus is on the rest of the season at the Scarlets and I will be working hard to try and play a role in achieving more silverware this season."