He's not sure yet who else will be part of the competition, though.
The Dolphins reached agreement with the former Jacksonville Jaguars quarterback after failed courtships with Peyton Manning and Matt Flynn. They also hosted San Francisco 49ers quarterback Alex Smith for a visit Sunday and may still consider signing him.
"They didn't say for sure they were bringing another guy in, but they said it's a possibility, whether in the draft or whatever," Garrard said in a phone interview.
For now, Garrard and incumbent Matt Moore are the contenders for the job.
"It's going to be a great competition, and I'm all about that," Garrard said. "I'm going to do my best to make sure it's me on opening day."
The Dolphins also told safety Yeremiah Bell he'll be released to create cap space, a person familiar with the discussions said. The person confirmed the discussions to The Associated Press on condition of anonymity because the Dolphins hadn't announced a move.
By cutting Bell, the Dolphins save more than $4 million in cap space, which could be used in negotiations with Smith.
The 34-year-old Garrard, a starter for Jacksonville from 2005-10, didn't play last season. He was released five days before the opener by the Jaguars, and Miami courted him last year after quarterback Chad Henne's season was ended by a shoulder injury.
But Garrard didn't sign, and instead underwent back surgery in October. He considered retirement, he said, but is now 100 percent and eager to extend his career another year.
"It was taken away from me, and it gave me a great perspective on life and this game," he said. "I want to make sure when I leave this game, I do it when I'm ready to go, and there's never any remorse or thought of, could I have done more?"
Garrard apparently impressed the Dolphins with his workout Monday, and he said he was impressed by new coach Joe Philbin and his staff.
"I just love the vibe," Garrard said. "I love everybody's mission and goal, and the purpose they have and the direction they're heading."
Garrard's best season was in 2007, when he threw 18 touchdown passes and only three interceptions. He topped 3,500 yards passing in 2008 and 2009, and he's 39-37 as a starter in nine seasons, all with Jacksonville.