Gutierrez arrived late Tuesday and passed his physical.
"He's a smart guy, he's been in some good systems," coach Lovie Smith said.
The Bears needed another quarterback in camp to back up Jay Cutler after Caleb Hanie sprained his throwing shoulder Saturday in San Diego. Hanie has been ruled out of Saturday's game against the Raiders, but he's expected to return in a few weeks. In the meantime, Gutierrez will try to get up to speed with the Bears offense.
"It's just part of the game, part of doing what we do as players," Gutierrez said. "We've got to deal with situations like this so I'm trying to come in and learn as fast as I can."
An undrafted free agent out of Idaho State, Gutierrez has attempted only two passes in three NFL seasons. Gutierrez will battle with rookie Dan LeFevour for the third quarterback slot. Smith anticipates that Gutierrez will learn enough of the offense that he might see a little action against the Raiders.
"I think he could learn enough," Smith said. "It's not like we're teaching him a new sport or anything like that."
Todd Collins and Josh McCown rejected Bears overtures to join the team. Trent Green and Damon Huard also reportedly turned down the Bears. New Bears offensive coordinator Mike Martz is now comfortable enough with Hanie that he didn't mind.
"Caleb is further than I thought he would be," Martz said. "You go through growing pains, we put a lot of pressure on him trying to get him ready and stress him out a little bit.
"He went through that phase and he's fought through it real well and he understands what we're doing."
Martz called the art of developing a backup quarterback an inexact science at best.
The offensive coordinator in St. Louis when the Rams won the Super Bowl following the 1999 season, Martz recalled how former Rams quarterback Trent Green was backed up by an unknown named Kurt Warner.
"Trent only threw two incomplete passes in that preseason, '99, and you have this grocery clerk back there as a backup quarterback [Warner]," Martz said. "So, who knows? I don't have a crystal ball."
The Bears also signed safety Aaron Webster. They waived guard Vince Vance and linebacker Matt Mayberry in order to reach the 80-man roster limit.
Michael C. Wright covers the Bears for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.