The parade kicked off at 11 a.m. as the team and their families made their way down Figueroa Street from the Shrine Auditorium on open-top buses, popping champagne bottles in celebration.
Kupp honored one of the city's most beloved athletes by donning a Kobe Bryant jersey.
"Kobe is synonymous with L.A. I feel it's only right - there's a championship, Kobe is a part of it," he said.
WATCH | Rams Super Bowl LVI victory parade - full coverage
Countless fans clad in a sea of yellow and blue lined the streets as the champions traveled toward the L.A. Memorial Coliseum, where the Rams played from 2016-19 while SoFi Stadium was being built. That's also where the team's home was when the Rams arrived in L.A. in 1946.
The Coliseum hosted the Super Bowl in 1973, and it was also home to the first-ever Super Bowl back in 1967.
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That's also where the parade culminated in a rally, with star players and coaches hyping up fans with enthusiastic speeches.
"We're here today to celebrate you guys for cheering for us all this time, and for us for making it happen when we needed to make it happen," said quarterback Matthew Stafford.
Sean McVay credits team in Super Bowl parade speech
Speaking to the crowd, head coach Sean McVay credited the entire team for bringing the championship title to L.A.
"The mental toughness, the resilience of this group - it took every single person. That's the best part about football, it's the greatest team sport there is."
"It's like a dream" said fan Lawrence Morse, who drove in from Irwindale with his 12-year-old son Jacob.
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"We watched almost every game the whole season," said Jacob. "We knew they would win the Super Bowl!"
The celebrating began Sunday when the Rams beat the Cincinnati Bengals 23-20 after a 79-yard final drive by Stafford that ended with a 1-yard TD toss to Kupp, the game's MVP.
Charles Goolsby, 16, came with his brothers and father. He said his late grandfather was a lifelong Rams fan and his passion for the team was contagious.
"I was holding my breath in the fourth quarter but I just knew that Kupp could win it," Goolsby said.
"We are here for our grandpa," he added.
This was the first victory parade in L.A. since the start of the pandemic. The Lakers and Dodgers did not get a parade after their championship wins in 2020.
The Associated Press contributed to this report.