The 32-year-old Williams was 9-10 with a 4.57 ERA in 37 games (25 starts) for the Angels in 2013, while working a career-high 169 1/3 innings. He joins Scott Feldman as experienced starters who have been added to Houston's young rotation this winter.
The Astros have not confirmed the deal is in place.
"We have a lot of young guys on the team, and I'm coming to a situation where I can help out the team, help out some guys and help get the Astros back where they used to be before, back in the days with the Killer B's and all those guys," Williams said, referring to the Astros' heyday a decade ago with Craig Biggio, Jeff Bagwell and Lance Berkman. "Hopefully we can get back to those days and get back to the winning ways."
The Astros will have to clear a spot on the 40-man roster to make room for Williams, who has a 4.35 career ERA in 155 games (117 starts) in eight seasons with the Angels, Nationals, Cubs and Giants. Twenty-nine of Williams' 38 career relief appearances have come in the past two seasons.
"In my eyes, all I want to do is go to camp and compete," he said. "That's the No. 1 thing with me. I want to go out there and compete. For me, I would love to start, but for the past three years, I've been doing both. It doesn't matter what the role is, as long as I go out there and help out the team. It doesn't matter if I'm in the bullpen or the rotation. I'm going to give it my all and go out there and do my best."
The Astros have added Feldman, Williams and Collin McHugh this offseason to a rotation that includes youngsters Brett Oberholtzer, Jarred Cosart, Brad Peacock, Dallas Keuchel and Lucas Harrell. Alex White could also be in the mix to start some games.
Williams, a native of Hawaii, just wants to help in any way he can.
"There's a lot of young talent in the organization, and I'm just happy and excited to see these guys shine," Williams said. "Hopefully I can help out the young guys and show them the way of being in the Major Leagues and being a great team and a great pitcher."
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.