"I'm excited," Grantham said Friday. "It's an opportunity to be a coordinator, coach in the SEC. They've won a lot of games there. They haven't quite been as good on defense as they would have liked over the past couple of years. Hopefully we can go in and get them back to being one of the premiere teams in the SEC."
Grantham's contract with the Bulldogs is for three years at $750,000 per season.
Grantham spent the past two seasons as the Cowboys' defensive line coach, helping nose tackle Jay Ratliff earn two Pro Bowl invitations and one All-Pro selection.
Grantham, the Cleveland Browns' defensive coordinator the previous three seasons, contributed to a defense that allowed the fewest points in the NFC this season.
ESPN.com's Chris Low writes about all things SEC in his conference blog.
Grantham will remain with the Cowboys through the playoffs, as his contract expires at the end of the season. The rest of the team's assistant coaches are under contract for next season. The Cowboys face Minnesota in an NFC divisional playoff game Sunday.
The Cowboys, meanwhile, announced Grantham's replacement minutes later, saying former Syracuse coach Paul Pasqualoni would fill the role. Pasqualoni, who was fired this week as the Miami Dolphins' defensive coordinator, was a Cowboys assistant for three seasons.
Grantham worked at Virginia Tech (1990-95) and Michigan State (1996-98) before spending the past 11 seasons in the NFL.
"I'm excited the search is over, we have our man, and look forward to what Todd will bring to our defense, our team, and our university," Georgia coach Mark Richt said. "I think it is particularly valuable that he has a wealth of experience on the defensive side of the ball at both the NFL and collegiate levels. Now we look forward to moving ahead with the home stretch of recruiting, finishing out the defensive staff, and getting ready for spring practice."
Grantham replaces Willie Martinez, who was fired Dec. 2 along with two other defensive assistants. His hiring ends a six-week search during which Virginia Tech's Bud Foster, LSU's John Chavis and Alabama's Kirby Smart were among those to turn down the Bulldogs.
This past season, Georgia ranked 10th in the SEC in points allowed (26.4) and seventh in yards allowed (328.4). In the past two years, the Bulldogs surrendered at least 30 points in 10 of their 26 games.
"There's potential there to win and win big," Grantham said. "So I feel like it was an opportunity I couldn't pass up."
Information from The Associated Press was used in this report.