Johnson said his foot got stuck in mud moments before he saw "the lunge" as the alligator grabbed his leg.
"He starts clamping down pretty tight, and he started to pull, and the next thing I do ... I poke [the gator] through the eye," he told WPLG-TV.
Johnson told Treasure Coast Newspapers that after he stuck his finger in the gator's eye, the reptile immediately let go and swam away.
After limping home with blood dripping from his leg, Johnson's wife cleaned the wound and wrapped the leg in a towel before taking him to a hospital.
Johnson said he suffered 12 puncture wounds that required 60 stitches, plus another five to mend the index finger that was cut on the gator's eye socket.
The Florida Fish and Wildlife Conservation Commission said a trapper captured the gator involved in the attack on Wednesday.
Officials said the alligator measured 8 feet, 6 inches and weighed nearly 250 pounds. The reptile has since been relocated to an alligator farm.
Johnson said that even though the reptile was trying to drag him into the water, staying calm was what helped him survive.
"You cannot panic," he told the paper. "I bass fish all the time, too. I'll reach down and lift up the bass with my hand. I just got lucky."
Johnson said when he's able to walk his dog again, he'll probably carry some sort of weapon for protection.
The Associated Press contributed to this report.