He will not play the rest of the preseason, however, because of a hairline fracture in his right thumb that will sideline him two weeks. Gabbert won't need surgery, but he will wear a protective brace while the bone heals.
Bradley said Gabbert will be back in time to prepare as the starter for the Week 1 opener at home against the Kansas City Chiefs.
"Normally a break would require surgery or six to eight weeks,'' Bradley said. "It's not the same with this injury. They feel like in two weeks he should have a chance to come back and begin his prep for Kansas City.''
Before the injury, Gabbert made a good case to wrap up the Jaguars' starting job, going 13-of-16 for 165 yards and a touchdown. He played the first four series in the team's exhibition opener against Miami, going 5-of-10 for 19 yards.
"It's a nice opportunity, but it doesn't end here,'' Gabbert said. "Gus always preaches competition every day and we compete against each other, but we're still going to go out there and put your best foot forward regardless of the situation.''
Henne completed 12 of his 21 preseason pass attempts in two games, with no touchdowns and an interception. He will start Saturday's preseason game.
"From my standpoint, it's disappointing,'' Henne said of losing the competition to Gabbert. "But I'm going to be the same person. I'm going to keep competing each and every day, try to better myself. I'm behind this team 100 percent. I'm behind Blaine. Whatever I can do to help is what I'm going to do.''
For his career, Gabbert has completed 54 percent of his passes for 3,876 yards, with 21 touchdowns and 17 interceptions. He is 5-19 as a starter.
Although Gabbert struggled at times in practice and did little in the preseason opener, his performance Saturday night was enough to convince Jacksonville's coaching staff that he's the guy. Bradley doesn't anticipate a quick change, either.
"The reason why we took this length of time is so that we would have some conviction and to stay strong,'' said Bradley, who was part of Seattle's staff that stuck with rookie Russell Wilson last season. "Russell, as the quarterback in the first couple of games, had to go through some learning and some growing, and that conviction was in place. I think it was really good for me to see how that entire process took place and the conviction and the support you need.''
Gabbert was expected to show improvement last year, but he played behind a patchwork offensive line and with two young receivers in Cecil Shorts III and Justin Blackmon. Jacksonville also lost star running back Maurice Jones-Drew to a season-ending foot injury in October.
Maybe the biggest difference this year is offensive coordinator Jedd Fisch's scheme. Having worked in a spread offense in college, Gabbert seems more comfortable in Fisch's system, which focuses on reading defenses before the snap and making quick decisions and throws.
"It's very quarterback-friendly and it puts a lot of responsibility on our shoulders because we do so much stuff at the line of scrimmage,'' Gabbert said. "It makes it fun for the quarterback to know that you have the ability to do some things.''
Information from ESPN.com's John Clayton and The Associated Press was used in this report.