Rogers has played 88 times for Scarlets as well as winning 13 caps for Wales, including scoring a hat-trick against New Zealand last November.
“The Ospreys have had a lot of success over the years and I’m really looking forward to testing myself in a different environment,” said Rogers.
“I’d also like to take this opportunity to thank all of the Scarlets fans for their support during my time at the club, it has always meant a lot to me.”
Despite the loss of a promising Wales international Davies said he remains positive about the current project to re-build a Scarlets squad who have struggled in URC this season.
“Our focus now is very clear. We are building a squad that is aligned, competitive and capable of driving this club forward,” he said.
“We have real strength and depth developing across the back three, with a group that combines international quality with exciting young talent coming through our pathway. That gives us a strong platform to build from.
“There is real momentum building here and we are excited about what lies ahead.”
