"No, not at all," said Williams, referring to the wintry conditions that essentially shut down most of the Buffalo region on Wednesday. "I spent four-and-a-half years in Chicago. I like the cold weather."
Williams then joked he was so eager to get the opportunity to play that he would sign anywhere.
"I'd go to Antarctica," he said. "But Buffalo's a lot better than Antarctica, so I'm just excited to be here."
The Bills did not disclose financial terms, but a source told ESPN NFL Insider Adam Schefter that the deal is worth $13.5 million, including $5.5 million in guaranteed money.
In signing the 6-foot-6, 330-pound player, the Bills addressed a significant need a day into the NFL's free-agency period. Williams will get the opportunity to fill the starting job at left guard, a position that was mostly unsettled last season.
Colin Brown opened last year as the starter, before being cut after six weeks. Doug Legursky finished the year at the position, but coach Doug Marrone still expressed dissatisfaction with the inconsistent production the Bills were getting at left guard.
"I am particularly excited about the direction our offensive line is moving in because we wanted to address this position," general manager Doug Whaley said in a statement released by the team. "We feel like we filled the need with a very good player."
Selected by Chicago with the 14th pick in the 2008 draft, the Vanderbilt product has had an up-and-down first six NFL seasons. He spent four-plus years with the Bears before having his contract terminated during the 2012 season. Williams then closed the year after signing with the St. Louis Rams, and then started all 16 games last season.
Overall, he's had 54 starts in 69 games.
Williams, who also has experience playing tackle, provides bulk and versatility to an offense that finished second in the NFL in rushing last season behind Fred Jackson and C.J. Spiller. The Bills (6-10), however, were held back mostly because of rookie quarterback EJ Manuel's inconsistencies, which were compounded by him sustaining three separate knee injuries.
The Bills targeted Williams before free agency began, and he made Buffalo his first visit by arriving in town on Tuesday night.
"We had some other teams interested as well," he said. "But this seemed like the best fit for me, and the opportunity I was definitely the most excited about."
Williams said he's grown from the experiences he's had since breaking into the NFL.
"I can't say I knew how to be a pro coming into the league when I did," Williams said. "Everything that happened in Chicago happened. But now I'm excited to move on. Getting cut is the most humbling experience anybody can have, much less a former first-round pick. But I learned from all those experiences."
ESPN.com Bills reporter Mike Rodak and The Associated Press contributed to this report.