In 26 appearances this season, the 32-year-old Williams is 1-4, having given up 7 home runs and 16 walks and striking out 38.
Williams played in six games for the Nationals in 2007 and didn't make another major league appearance until five years later, when he signed with the Los Angeles Angels.
"I've been doing it for the last three years, and the road that I went through, I don't think nobody would ever try and come back," an emotional Williams said, according to MLB.com. "I'm sorry I'm getting emotional right now, but the way I go out there and do my business, and the road I went through, nobody could do it like I did. I'll always have the strength to keep on going."
Williams signed a $2.1 million, one-year contract in February. He was 9-10 with a 4.57 ERA in 25 starts and 12 relief appearances last year for the Angels, including a 4-0 record in five September starts. He has a 42-47 record and a 4.35 ERA in eight seasons with San Francisco (2003-05), the Chicago Cubs (2005-06), Washington (2007) and the Angels.
The Associated Press contributed to this report.