Daniel Davillier, Beckham's lawyer, released a statement confirming no charges against the 27-year-old have been sought because the security officer from New Orleans Police Department involved does not want to pursue the matter.
The warrant had been obtained on Thursday after an alleged incident that occurred at the Mercedes-Benz Superdome on Monday.
NFL star Beckham appeared to slap the officer's buttocks in the LSU locker room during the celebrations after their 42-25 victory over Clemson in the National Championship Game.
"The arrest warrant stemming from the postgame locker room celebration at the Superdome on January 13, 2020, has been recalled; there is no warrant outstanding for the arrest of Odell Beckham, Jr.," Davillier confirmed in a statement to Omnisport.
"The security officer involved does not wish to pursue charges in this matter. This legal matter has been resolved."
The Browns released a statement of their own saying on Thursday revealing they had contacted their player regarding the warrant, insisting he was "cooperating with the proper authorities".
While one matter has now been resolved, Beckham still faces scrutiny for another incident that took place at the game, having been spotted handing out notes to players on the field.
The NCAA has rules that bar college players from receiving certain benefits.
Having initially said they believed the bills to be fake, LSU later released a statement saying "information and footage received since shows apparent cash may have also been given to LSU student-athletes" and that they had contacted NCAA regarding that incident.
Beckham spent three years with LSU between 2011 and 2013, accumulating 2,340 receiving yards and catching 12 touchdowns.
Beckham went to three straight Pro Bowls with the Giants and was traded to Cleveland back in March.
In his debut season with the Browns, the 27-year-old had 74 catches for 1,035 yards and four touchdowns - the lowest totals he has achieved across a full 16-game season.