The move will get Smart closer to his career goal of being a defensive coordinator in college or the NFL, he said.
"I'd never thought about coaching in the NFL," he said. "It was an opportunity for me to get back on the defensive side of the ball. If I was going to be hired as a defensive coordinator, I would have to be hired from a defensive position. I wasn't going to get hired from an offensive position."
Saban contacted Smart on Tuesday just as Smart, 30, was preparing to fly to New York for an interview with the New York Jets. New York coach Eric Mangini talked with Smart about the Jets' linebackers/nickel backs coaching job, and Smart then flew to Miami for an interview Wednesday.
"I was completely happy with the job I had," said Smart, who was a four-year letterman for the Bulldogs and an All-SEC safety in 1998.
At Georgia, Smart was coaching on the offensive side of the football for the first time in his career. He coached defensive backs for Saban at LSU in 2004. At Miami, he will be on a staff that includes former NFL head coaches Dom Capers and Mike Mularkey.
"I feel like I learned more this year than I ever have any year I've been coaching," he said.
"That was the hardest, telling them," he said.
Like all of Georgia's assistant coaches, Smart was set to receive a raise this year. His salary would have increased to $137,500, but he is expected to make more than $200,000 as an NFL assistant coach.
"Money was never an issue," he said.
Georgia coach Mark Richt hopes to have Smart's replacement hired by the start of spring practice on March 4, Richt said. He said he has a list of potential candidates in mind but did not name them.
"Kirby did a great job with our backs during the past year," Richt said. "We hate to lose him but at the same time recognize the opportunity he has and wish him nothing but the best."
Now Georgia has to wait and see if Garner also leaves. The Bulldogs' recruiting coordinator/defensive line coach/assistant head coach had an interview with the New Orleans Saints last week. Georgia insiders don't expect Garner to leave, but Richt did not rule it out Friday evening.
"I don't have an answer on that," Richt said. "Until he tells me, I don't know."
Garner did not return a telephone message left at his office. Garner's pay will be raised from $210,000 to $231,000 this season, and athletic director Damon Evans declined to say if the school would raise Garner's pay even further to keep him in Athens.
"It's getting to the point where we really can't compete with the NFL because their salaries are so high," senior associate athletic director Frank Crumley said.
As part of Richt's new $16 million deal, all of the Bulldogs assistants were approved for pay raises. Defensive coordinator Willie Martinez will be the highest-paid assistant at $260,000, followed by Garner, offensive coordinator Neil Callaway ($203,500), wide receivers coach/associate head coach John Eason ($170,500), defensive ends coach Jon Fabris ($170,000), tight ends coach David Johnson and quarterbacks coach Mike Bobo ($143,000) and linebackers coach John Jancek ($137,500).
The total compensation of $1.6 million "should put us in the top 10 in the country when you take the total salary pool," Crumley said.