The veteran swingman asked for and was granted his release from the San Antonio Spurs earlier this week. He will earn a prorated portion of the veteran's minimum of $1.1 million.
"I think he has basketball left in him," Rivers said. "What
he can give us and how it fits, we'll figure it out as we go."
Finley, who turns 37 Saturday, sprained his left ankle early this season and appeared in just 25 games for San Antonio. He had fallen out of the Spurs' rotation, prompting him to request to be waived.
Finley's stats have dipped dramatically this season (3.7 points, 1.5 rebounds, 0.8 assists over 15.8 minutes per game), but he's regarded as one of the best locker-room presences in the league, and he boasts 111 games of playoff experience, winning a championship with the Spurs in 2007.
For his career, Finley is a 37.4 percent 3-point shooter (though he's only shot 31.7 percent from beyond the arc this season), and he has the potential to give the Celtics another perimeter threat after moving Eddie House at the trade deadline.
Last year in the playoffs, Finley averaged 8 points, 3 rebounds and 1 assist per game in five games with the Spurs. For his career, those numbers spike to 13.6 points, 4 rebounds, and 2 rebounds per game in the postseason.
A two-time All-Star, Finley will find himself behind Paul Pierce and Marquis Daniels at the small forward position, but his presence might allow the Celtics some flexibility with Daniels, who can play either guard spot or small forward.
In a season in which both Pierce and Daniels have been nagged by injuries, Finley also provides insurance should the injury bug not fly far from the Celtics.
"He's a veteran who can spread the floor and shoot pretty
well," Pierce said. "He brings a lot of experience. He's a
veteran who has been around the block a few times. I'm sure he'll
find his way, and he's played in a lot of big games during his
career. He knows how to approach them and play in them. Experience
can always help in tight situations."
Celtics president of basketball operations Danny Ainge confirmed his interest in Finley Wednesday in an interview on Boston sports radio station WEEI, saying he would be another shooter off the bench who could fill in for Pierce or Allen, and that having that extra option could be useful for Rivers. But he also played down the potential impact Finley would have.
"I certainly don't consider Mike Finley to be someone that's going to make the difference in us winning the championship," Ainge said, adding that he doesn't want to put that kind of pressure on the veteran. "That's why I keep the pressure on our starters."
Finley and Rivers should be fast friends. The pair both grew up outside Chicago and attended Proviso East High School in Maywood, Illinois.
"I don't think a veteran ever hurts," Rivers told the Boston Globe earlier this week when rumors first began to swirl about the Celtics' potential interest in Finley. "I think it always helps your team to have one, if it's the right one. Every team has some holes. Shooting is one thing we can't have enough of as far as I'm concerned. You look at some of these other teams, their shooting is ridiculous."
Even after adding Finley, the Celtics still have one empty roster spot.
ESPN.com senior NBA writer Marc Stein, ESPNBoston.com's Chris Forsberg and The Associated Press contributed to this report.