Williams, 30, will cover for Anscombe and the injured Stephen Myler for the rest of the campaign having left Worcester Warriors. He previously played for Leicester Tigers, Gloucester and in Japan.
The three-times capped Welsh international will compete with the Ospreys one fit No 10, Jack Walsh, for the first-team spot at the Swansea.com Stadium. The Ospreys have welcomed the addition of a player with vast experience and leadership qualities.
“I’m really looking forward to getting started here, the Ospreys have a rich history and a great squad that are capable of going on and becoming a real force,” said Williams.
“I spoke with the coach before making my decision, and it was clear to me that he had a plan for how I will fit in to the wider vision for the team going forward. It’s been a while since I’ve played my rugby in Wales, but I can’t wait to be back in the region where it all started for me.”
The Ospreys face one of Williams’ former clubs, the Leicester Tigers, in their first Heineken Champions Cup Pool fixture on Sunday. Williams made more than 100 appearances and scored more than 600 points during his time at Welford Road.
“For us to compete at the highest level, it is hugely important that we have quality depth where we need it,” said Ospreys head coach, Toby Booth. “Signing Owen not only provides injury cover for us, but also improves us a group.
“Jack Walsh has done a great job stepping up at 10 in some huge games for us over the last few weeks, but ultimately with Gareth’s injury, we needed to reinforce in that area.
“Owen can play 10 or 12 and brings a wealth of experience with him from his time in Premiership. I have no doubt that he will make a positive impact in a variety of areas for us.”