CLEVELAND — After rattling off several reasons for signing with the Cavaliers, Deron Williams got around to the one that matters most.

He wants a ring.

"Competing for a championship is something that I haven't had a chance to do," he said.

Williams, an Olympian and three-time All-Star who has never made it to the NBA Finals, signed as a free agent on Monday with the Cavs, giving the defending champions the backup point guard they've coveted and another playmaker to help them defend their title.

Williams will initially come off the bench for the Cavs, who have been seeking a backup for All-Star Kyrie Irving all season. A 13-year veteran, Williams had his contract bought out last week by Dallas, cleared waivers on Saturday and told the Cavs he would sign with them.

As he stood outside the Cavs' locker room, Williams, who played on two U.S. Olympic teams with LeBron James, already looked at home.

"I just felt like this was the best fit for me," he said. "It was a team that showed interest in the offseason in signing me. ... I think my name was thrown around all season and so I know a lot of the guys on the team. You know playing with LeBron in the Olympics. I played with Kyle (Korver) and he's one of my good friends and we still talk until today. I just feel like I'll be comfortable here. I'll have a significant role here."

Williams said he's willing to play fewer minutes to help the Cavs win, although he joked that general manager David Griffin promised him he would start.

And his signing may not be the last for Cleveland, which has expressed interest in center Andrew Bogut, who was waived by Philadelphia.

Williams played with Bogut and smiled when asked if he had any pull in getting the big man signed by the Cavs.

"We've been in contact," he said.

Cavs coach Tyronn Lue will likely have Williams run the offense for Cleveland's second unit, plus Williams will allow the Cavs to rest both Irving and James, who returned to the lineup on Monday against Milwaukee after missing one game with strep throat. Down the line, Lue could use Williams in the starting lineup, but for now, Williams is happy to contribute any way he can.

"It was kind of an easy decision for me," he said. "I definitely looked at a couple other teams. But once Dallas informed me they kind of wanted to go in a different direction, the Cavs were the first team that jumped out at me. A lot of times you overthink things. I kind of went with my first thought."

Williams has averaged 16.6 points and 8.2 assists in his career since debuting with Utah in 2005. He and Korver were teammates for three years with the Jazz, reaching the Western Conference finals in 2006-07.