The 30-year-old left-back made 46 appearances last season but failed to feature this campaign and his contract was terminated by mutual consent on deadline day.
"It's a deal that suited all parties," Yates told BBC Gloucestershire. "The club came and put something to Billy and myself so that we could part.
"We just felt he'd hit a brick wall and didn't feel that he could contribute. Last season took a lot out of him and he was fantastic for us.
"With a squad like ours we can't have any passengers. He's a great lad to have around but we weren't looking to use him.
"We wish Billy all the best and thank him for his time here."
- Sports & Recreation
- BBC Gloucestershire