They will meet the Green Bay Packers - who claimed their second consecutive NFC Championship by defeating the San Francisco 49ers 23-10 at Candlestick Park - at San Diego on 25 January.
The Broncos were led by their running back Terrell Davis who gained 139 yards rushing - the first time this season the Steelers have given up more than 100 yards - and a touchdown. John Elway threw two touchdown passes in the final two minutes of the first half. That put them 24-14 ahead at half-time.
Pittsburgh, hosting their third AFC Championship in the past four years, fought back with Kordell Stewart throwing a touchdown pass with less than three minutes remaining.
He had opened the scoring, running in for a touchdown but the quarterback's most crucial statistics were three interceptions and a lost fumble.
The Denver kicker, Jason Elam, accounted for the Broncos' only points after the break, his field goal proving to be the match-winner.
The victory puts Elway and the Broncos, a wild-card team, back in the Super Bowl for the first time since 1990 when they lost to San Francisco. Elway was also on the losing side in his other two Super Bowl appearances, against Washington and the New York Giants.
Green Bay, despite playing away from the friendly confines of Lambeau Field where they had won 27 consecutive games and never lost in the play- offs, were never threatened in a match played in torrential rain.
Ryan Longwell kicked three field goals and Brett Favre connected with Antonio Freeman for a 27-yard touchdown pass. Dorsey Levens also added a late touchdown run to seal the victory.
The Green Bay defence dominated, limiting the Niners to a single field goal and never allowed San Francisco to establish any type of running attack. The 49ers' other points came from a 95-yard kick-off return for a touchdown by Chuck Levy.
Green Bay are becoming something of a bogey team for the 49ers. Sunday's win was the third consecutive year the Packers have knocked them out of the play-offs.
Green Bay will be bidding for their second straight Super Bowl title under the coach Mike Holmgren, who said: "Brett Favre played great. We are used to this kind of weather, but this was real bad."
Favre said: "I only play this game to get to the Super Bowl and win it. The weather was really rough, but the receivers did a great job holding on to the ball. At times that was more than I did."
The Packers are already favourites to win the Super Bowl. An AFC team has not won it since 1984, when the Los Angeles Raiders defeated the Washington Redskins.
The Indianapolis Colts have named Jim Mora, formerly of the New Orleans Saints, as their new head coach.