The Texans never have had a winning record, and Carr often was the scapegoat. He completed 60 percent of his passes, but also threw 65 interceptions and was sacked 249 times in five seasons.
Houston hoped Carr would flourish under new coach Gary Kubiak last season, but the Texans went 6-10.
Williams, formerly Domanick Davis, is Houston's career rushing leader with 3,195 yards. He spent all of last season on injured reserve with a knee injury.
Also Friday, the Texans re-signed 1999 Heisman Trophy winner Ron Dayne, who joined the Texans just before last season and blossomed late in the season, rushing for 429 yards and five touchdowns in December.
The Texans released Carr a day after signing Matt Schaub and saying he would be their starting quarterback. General manager Rick Smith said Thursday the team was trying to trade Carr, who had two years left on a contract that was to pay him $11.5 million for those seasons.
"It will be kind of weird without David next season, especially for the guys that have been there for a long time," Dayne said in a phone interview. "It won't be that big for me since I just got here. But we've got to move forward without him."
A message left for Carr's agent, Mike Sullivan, was not immediately returned Friday. The team said it would have no immediate comment.
Williams sat out most of training camp last season with soreness in his right knee. He showed up in the Texans' locker room on Jan. 1, saying he had legally changed his last name from Davis to Williams, his mother's maiden name.
He missed five games in 2005 before undergoing arthroscopic knee surgery. He returned for training camp and declared himself healthy, but soon stopped practicing because of a bone bruise in the knee.
The Texans bolstered their backfield by signing Ahman Green earlier this month. The same day, Smith said Williams had experienced more swelling in his knee and will probably undergo another surgery.
The Texans signed Dayne two days after placing Williams on injured reserve in September. Dayne had been released by Denver, where Kubiak was formerly the offensive coordinator.
Dayne led the Texans with 612 rushing yards on 151 carries, his best season since 2001 with the New York Giants. He ran for 153 yards and two touchdowns in Houston's 27-24 win over Indianapolis on Christmas Eve, one of the biggest wins in franchise history.
Dayne said he's content to back up Green, a four-time Pro Bowler.
"It's OK," Dayne said. "I've been in the same position for most of my career. So I've been used to it. Whenever I get in I just want to do my best and help the team."