Grantham will receive a five-year guaranteed contract worth $1 million per year, according to a source.
Grantham was defensive coordinator at Georgia for four seasons, installing a 3-4 scheme that led to increased sacks and takeaways.
He previously coached in the NFL with Dallas, Cleveland, Houston and Indianapolis and previously in college at Michigan State and Virginia Tech.
Among the coaches Grantham has worked with are Frank Beamer, Bud Foster, Nick Saban, Romeo Crennel, Dom Capers and Wade Phillips. In 2011, the Georgia defense finished fifth nationally in total defense.
Louisville this week hired Bobby Petrino as head coach entering the Cardinals' first season in the ACC.
A source told ESPN's Brett McMurphy last week that Kevin Steele, who spent last season as Alabama's director of player personnel, would join Petrino's staff as coordinator. Multiple news outlets later reported Steele turned down an offer for the position.
Former UAB coach Garrick McGee, who served as Petrino's offensive coordinator at Arkansas, will join Petrino's staff to run the offense at Louisville.
Richt said he already has heard from possible candidates to replace Grantham.
"We are appreciative of all the contributions Todd has made to our program and wish him nothing but the best," Richt said. "But at the same time the opportunity to work at Georgia is extremely attractive and there already is, and will be, interest from some very, very outstanding coaches.
"We have a lot of defensive players coming back, as well as some outstanding defensive recruits, and there's going to be plenty of interest in coaching them. I'm excited about the prospects of a great defensive coordinator being on board as quickly as possible."
Georgia expects to return 10 starters on defense.
Grantham is the second defensive assistant to leave Richt's staff. Secondary coach Scott Lakatos resigned Thursday, citing undisclosed personal reasons.
Information from The Associated Press was used in this report.