Heupel is finishing his second season at Missouri, which has put up big offensive numbers.
"Coach Frost did an outstanding job," Heupel said Tuesday at his introductory news conference. "My job to continue to develop those relationships and continuity. I look forward to that. We need to play smart football but we also have to be physical."
Heupel flew to Orlando on Monday night to meet with athletic director Danny White and Randy Shannon, who will be the Knights' new defensive coordinator.
The 39-year-old Heupel served as quarterbacks coach and co-offensive coordinator at Oklahoma from 2006 to 2014 before being let go at his alma mater, where he played quarterback on the Sooners' national championship team in 2000 and was the Heisman Trophy runner-up.
He spent the 2015 season at Utah State before joining Missouri's staff.
"I believe we've identified one of the brightest offensive minds in college football," White said in a prepared statement. "His offensive system is very similar to what we've been running. I know he's going to utilize all the great talent on our roster and continue to add to it. He's no stranger to success, winning a national championship as a quarterback and leading a number of extremely high-powered offensive teams."
Missouri improved from 124th nationally in offense the year before Heupel arrived to 13th last year and seventh this season, averaging 511.5 yards and 39.3 points per game.
UCF also announced that Heupel is hiring Shannon as his defensive coordinator, which is the same job he had with Florida this past season.
Shannon served as the Gators' interim head coach after Jim McElwain was fired. He also served as Miami's head coach from 2007 to 2010 after serving as the school's defensive coordinator.
"When I was first contacted I poured over some guys who I wanted." Heupel said. "Me being an offensive guy, getting the right hire on defense was critical. I have competed and coached against Randy. He plays a 3-4 scheme and believes in multiple coverages. Has a rich history in Florida and recruiting and that's the lifeblood of our program."
The Knights are 12-0 and won the American Athletic Conference title Saturday. The Knights will play Auburn in the Chick-fil-A Peach Bowl in Atlanta on Jan. 1, with Heupel saying he will watch from a booth at Mercedes-Benz Stadium.
Heupel, who runs a no-huddle, fast-paced style of offense, said he was able to catch "bits and pieces" of UCF's play this season.
"There are special players coming back when you look at the roster. For the most part the nucleus on both sides of the ball are coming back," Heupel said. "There is a great quarterback coming back who made plays with both his arms and legs. Always great to have that piece coming back."
UCF had targeted former Texas A&M and Houston coach Kevin Sumlin for its job, but talks didn't progress on Sunday and the school turned its attention elsewhere.
Knights offensive coordinator Troy Walters, named acting head coach after Frost's departure Saturday to Nebraska, interviewed for the job. It's unclear whether Frost or Walters will coach UCF in the bowl game.