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Cincinnati came from 21-3 down to win the AFC Championship game 27-24 at the much-fancied Kansas City Chiefs.
The Rams recovered from 17-7 behind to beat the San Francisco 49ers 20-17 to lift the NFC Championship.
Super Bowl 56 takes place at the Rams' So-Fi Stadium on 13 February.
The Rams' triumph means a Super Bowl will feature a home team for the second successive year after the Tampa Bay Buccaneers beat the Chiefs at Raymond James Stadium in 2021.
The Rams also made history by becoming the first team to overturn a double-digit fourth-quarter deficit in a Championship game to cap another thrilling play-off weekend, following a divisional round that saw all four games decided by last-second field goals or overtime.
Earlier, defending AFC champions Kansas City were heavy favourites to book a third successive Super Bowl appearance and appeared to be cruising to victory when they opened up a 18-point lead over Cincinnati.
But the Bengals made a crucial stop just before half-time to limit their deficit, which quarterback Joe Burrow clawed back during the second half as his opposite number Patrick Mahomes began to go awry.
Before this season, Cincinnati - who were the worst team in the NFL two years ago with a 2-14 record - had not won a play-off game in 31 years but they have now won three in quick succession.
Kyle Shanahan's 49ers had enjoyed six successive victories over their NFC West divisional rivals, including an overtime win in the final game of the regular season that secured their play-off spot.
On that occasion, San Francisco rallied from 17-0 down but the roles were reversed on Sunday as the Rams scored 13 unanswered fourth-quarter points, aided by some individual errors by the 49ers.
Both quarterbacks were far from their best, the Rams' Matthew Stafford throwing an early interception to Jimmy Ward before making amends by finding Cooper Kupp in the endzone to put the hosts ahead.
But a superb solo score from Deebo Samuel, who beat several defenders on a 44-yard run, and a Robbie Gould field goal punished several miscues from the Rams to give the 49ers a 10-7 half-time lead.
When tight end George Kittle hauled in a pass from Jimmy Garoppolo late in the third quarter, that advantage was stretched to 10 but the Rams replied immediately with influential wide receiver Kupp's second touchdown.
The 49ers wilted under the pressure as Jaquiski Tartt dropped a straightforward interception that could have killed the game and, after two Matt Gay field goals put the Rams ahead, Garoppolo was picked off with a minute to go to send the Rams to a second Super Bowl in four seasons.
Only 15 months separate Burrow and Mahomes in age but the latter has already won two AFC titles and a Super Bowl, while this year has marked the Bengals quarterback's first post-season campaign.
That difference in experience appeared to be telling in the first half as Mahomes led the Chiefs to three touchdowns on their opening three drives as Burrow struggled to get a foothold.
A 10-yard pass to Tyreek Hill opened the scoring and although Cincinnati responded with an Evan McPherson field goal, the Chiefs quickly added two more touchdowns.
Wide receiver Mecole Hardman was central to both, reeling in a 44-yard Mahomes pass on a drive that ended with a touchdown for tight end Travis Kelce before scoring himself with a smart catch from an improvised close-range bullet.
But AFC North champions Cincinnati have been arguably the NFL's most improved team this season, and Samaje Perine's 41-yard catch and run reduced their deficit to 11 points.
The game turned on the brink of half-time as, with five seconds remaining, Kansas City turned down the chance of a close-range field goal to go for a touchdown and Hill was tackled short of the line.
That decision proved costly as Kansas City were unable to regain the momentum after the interval with the previously-unflappable Mahomes coming under regular pressure.
McPherson hit another field goal and, after Mahomes was picked off by BJ Hill, Cincinnati levelled as Burrow found Ja'Marr Chase for a touchdown and Trent Taylor for a two-point conversion.
McPherson converted a 52-yard kick to give the Bengals the lead for the first time but Mahomes recovered his composure to lead a solid Chiefs drive that ended with Harrison Butker's last-second 44-yard field goal.
Butker had forced overtime the previous week as Kansas City edged out the Buffalo Bills but there was to be no repeat as Mahomes was picked off by Vonn Bell when throwing downfield.
Rookie kicker McPherson, just as he had in the Bengals' previous post-season wins over the Las Vegas Raiders and Tennessee Titans, proved the hero by kicking the decisive field goal from 31 yards.
