The Sacramento Bee first reported the development, and it was confirmed by ESPN.
To get the green light to practice by the team, the 49ers medical staff must agree with the assessment of Dr. Peter Millett, who examined Kaepernick on Tuesday.
Kaepernick was limited during organized team activities and minicamp after undergoing offseason surgeries on his left shoulder, left knee and right thumb. The 49ers begin training camp practices Sunday.
Millett, who performed Kaepernick's shoulder surgery, gave the quarterback the OK after putting him through a series of tests, a league source told the Bee. According to the newspaper, doctors were waiting to clear Kaepernick until he got back some of the weight and strength he lost while recovering from the surgeries.
Kaepernick was a regular attendee of the 49ers' offseason workouts and said at the team's three-day mandatory minicamp in June that his only focus was on getting healthy and reclaiming the starting job after a tumultuous offseason that also included a trade demand, followed by a proposed trade with the Denver Broncos that fell apart.
Kaepernick, who helped guide San Francisco to two consecutive NFC Championship Game appearances, went on injured reserve in late November last season, and Blaine Gabbert took over the quarterback job. Gabbert took almost all the reps with the 49ers' first-team offense during offseason workouts and minicamp, while rookie sixth-round draft pick Jeff Driskel and free-agent addition Thaddeus Lewis worked with the backups.
That has put Gabbert miles ahead of Kaepernick in terms of learning new coach Chip Kelly's system, although Kaepernick tried to stay up to speed by going through the physical motions of his dropbacks and reads while standing behind the rest of the offense.
Kaepernick said in June that he expects an open competition when the 49ers open training camp.
"They haven't said anything about pecking order or anything like that," he said. "All I've heard is Chip has told me it's going to be a competition ... and to come in and be ready to compete. That's going to be my mindset, and I'm excited to do that.
"I'm ready to give this team everything I have. It was a great feeling to be out there this week. The fan support that I've gotten through everything and especially seeing people out, the support that I've gotten was amazing. It's made me really excited to be out here and play."