Stafford told reporters that he hopes to play with the Rams "for a long time."
"I want to be playing in those big games and those big moments," he added. "For me, it's an opportunity more than anything."
Stafford was effusive with praise for his new wide receivers, Robert Woods and Cooper Kupp, and what the Rams offense can look like in 2021.
"They do an outstanding job of getting open," he said. "It's pretty impressive to watch those guys go. They both do it in their own unique way, both have an understanding of the game (that) jumps out on tape. Once they have the ball in their hand, they do a great job of running after the catch, which is huge in this league."
Stafford's current deal runs through the 2022 season. He is scheduled to earn a combined $22 million in base salary over the next two years, plus $10 million roster bonuses in each season.
Per NFL Network's Ian Rapoport, Stafford didn't require a contract adjustment or extension as part of the trade to Los Angeles.
After reportedly agreeing to acquire Stafford in January, the Rams officially announced the deal Thursday to send Jared Goff and two future first-round draft picks in 2022 and 2023 in exchange for the 33-year-old.
The deal came about after Stafford requested a trade from the Lions in January, per NFL Network's Tom Pelissero. He spent 12 seasons in Detroit after being selected No. 1 overall in the 2009 draft.
Stafford has thrown for 45,109 yards with 282 touchdowns and a 62.6 completion percentage in 165 starts with the Lions. He led the franchise to three playoff appearances in 2011, '14 and '16, and the Georgia product made his only Pro Bowl in 2014.
The Rams were looking for an upgrade at quarterback after Goff had disappointing seasons in 2019 and 2020. The two-time Pro Bowler threw for 8,590 yards, 42 touchdowns and 29 interceptions in 31 games over the past two years.
Los Angeles made the playoffs last season with a 10-6 record but lost to the Green Bay Packers in the NFC Divisional Round.