Kendricks is facing a possible prison sentence after he pleaded guilty to insider trading charges.
"We had done a lot of homework on it," Carroll said Saturday. "It happened 4 1/2 years ago, so it's a story that's been worked on for a long time. There's a lot of good information. We've come to learn who he is and what he's all about and how remorseful he was and how he admitted to his mistake a long time ago -- he paid the money back, he did all of the right things along the way.
"The process continues, but we just checked everything we could possibly check out, and he's a guy that deserves a second chance."
Kendricks' sentencing hearing is set for Jan. 24.
The NFL already has suspended Kendricks, but the ban has been appealed and is expected to be heard in the next 10 days or so, ESPN reported.
Kendricks, 27, said he's willing to give his all for the Seahawks.
"As of right now, I have an opportunity, and I want to make the most of that," he said.
Carroll confirmed that Kendricks will play Monday night against the Chicago Bears (0-1). The Seahawks (0-1) have been decimated by injury, with middle linebacker Bobby Wagner (groin) and weakside linebacker K.J. Wright (knee) having been ruled out for the contest.
"He's going to play," Carroll said. "The background that he has and the instincts that he has, and he has been coached really well over the years, he really has a chance to pick it up really quickly and get in there and help us. He had three really good days and studied like crazy with the coaches, and he's ready to help us out."
"It's been pretty hard," Kendricks said. "It's been very hard. But I'll overcome this just like I've overcome other obstacles in my life. But like I said, I'm very blessed to have this opportunity, so I treat it as such. But football is helping me a lot."
Kendricks allegedly made a profit of nearly $1.2 million from investments tied to insider trading four years ago. Damilare Sonoiki, a Goldman Sachs analyst who was charged with assisting Kendricks, also pleaded guilty.
A second-round pick of the Eagles in the 2012 NFL Draft, Kendricks spent his first six seasons with Philadelphia before he was released by the team in May. He signed a one-year deal with the Browns the following month.
Kendricks recorded 77 tackles, two sacks and six pass breakups in 15 games last season for the Eagles. He has collected 459 tackles, 14 sacks and three interceptions in 85 career contests for Philadelphia.