The afternoon started with plenty of jokes.

Los Angeles Rams cornerback Jalen Ramsey posted a coy picture on Twitter with the caption: “Hehehehehe.” Rams Coach Sean McVay, when asked by reporters if the team had interest in signing the free agent receiver Odell Beckham Jr., deflected the question. But as he stood at the microphone, he grinned.

Less than an hour later, the deal for Beckham was finalized. Beckham, a three-time Pro Bowl receiver and the 2014 offensive rookie of the year, agreed to terms with the Rams, the team announced. The move is the latest by the Rams’ general manager, Les Snead, in an attempt to build a championship roster with proven veterans, regardless of consequences to the team’s finances and draft capital.

The Cleveland Browns released Beckham, 29, last week amid tension between him and quarterback Baker Mayfield. The two did not develop on-field chemistry during Beckham’s three years in Cleveland, and the receiver’s father posted a compilation video on social media of Mayfield either misfiring or not throwing the ball toward Beckham when he was open.

Beckham, drafted No. 12 overall by the Giants in 2014, quickly became one of the N.F.L.’s biggest stars after securing a one-handed touchdown catch against the Dallas Cowboys with the ball at his fingertips. But the Giants traded him in 2019 for first- and third-round picks in that year’s draft and for safety Jabrill Peppers. After the Browns could not find a trade partner last week, they released Beckham, and he went unclaimed on waivers.

The signing escalates the pressure on the Rams to win a Super Bowl. The game will be held at the end of this season in their home venue, SoFi Stadium in Inglewood, Calif. Ten days ago, Snead traded with Denver for Von Miller, an outside linebacker who is an eight-time Pro Bowl selection and who was chosen as the most valuable player of the Super Bowl in the 2015 season. The Rams are 7-2 and in second place in the N.F.C. West.

This off-season, Snead acquired quarterback Matthew Stafford from the Detroit Lions in exchange for quarterback Jared Goff and draft picks, including two in the first round. In 2019, Snead traded for Ramsey, one of the best cornerbacks in the league, in a deal with the Jacksonville Jaguars that cost the Rams two first-round draft picks and one in the fourth round.

Snead’s philosophy has been to rely on veterans with elite credentials and to collect them by doling out draft picks. Now, with a talent-laden roster, the Rams have a chance to prove that their method works.