He is the official starter as of this moment (heading into camp). Bell and Hearst both could get a substantial amount of play, though, and Bell could take the starting job outright.
EDIT: I'll add the article from Fanball I'm basing that off of:
ESPN's John Clayton is reporting that second-year back Quentin Griffin is the frontrunner to replace Pro Bowl running back Clinton Portis as the Broncos' feature back. Griffin ran with the first team at the team's recent minicamp, and his 28-carry, 136-yard effort at Indianapolis in week 16 is reportedly etched in coach Mike Shanahan's memory. The Broncos also signed veteran Garrison Hearst in free agency this offseason and selected Oklahoma State star Tatum Bell in the second round of the draft.
Griffin has elite speed, but the knock on him is his size. At 5-7, 195 pounds, he is a good four inches shorter than Portis, although only 10 pounds lighter. The minimal weight differential bodes well for his ability to take the pounding that a feature back endures, but it's still a bit on the light side. We're also not overly impressed with the fact that Griffin ran with the first team; Hearst (5-11, 215 pounds) is learning a brand new system and Shanahan wouldn't insert Bell (5-11, 212 pounds) into the starting unit at his first-ever minicamp. We'll upgrade Griffin on our cheat sheet since he is seemingly the frontrunner, but we're still ringing the Bell as our favorite to win the job long-term. Remember, both Portis and Mike Anderson rushed for 1,500 yards in their rookie seasons under Shanahan.