The suspect is the former director of the tabloid La Prensa, Mauricio Ortega, according to the company that owns the paper, OEM, as well as the Mexican Attorney General's office. The AG's office said that he has not been detained because no charges have been filed.
OEM said Ortega resigned March 14, citing "personal reasons" and the resignation was accepted, according to a company statement. But the company said it was surprised to learn about the allegations, saying Ortega "took advantage of his position and used La Prensa to obtain a media credential to access the field, press conferences and other areas of the NGR stadium."
A source told ESPN that footage from Fox showed Ortega going into the locker room, allegedly reaching into Brady's bag and taking the jersey. The source said officials reviewed 20,000 credentials, leading them to Ortega as a person of interest.
The NFL, which did not name the suspect, said the jersey was part of a larger haul that was in the possession of a credentialed member of the press.
In a statement today, Brady said he was happy that the case had come to a resolution.
“I am happy my jerseys from SB 49 and SB 51 have been recovered, and I want to thank all of the law enforcement agencies involved," he said. "I know they worked hard on this case – and it is very much appreciated. Hopefully when I get the jerseys back I can make something very positive come from this experience."
"Proud @houstonpolice Major Offenders Divison traced Brady Jersey to Mexico & it has been recovered with help of FBI & Mexican authorities," Acevedo wrote.
Mexican officials have not issued a formal statement but a spokesperson for the Mexican Attorney General’s office told ABC News that Mexico's Attorney General carried out a search last week and handed over the jersey to the U.S. authorities.
News of the missing jersey first surfaced when Brady told team owner Robert Kraft in an on-camera locker room conversation after the game that he was unable to locate the jersey he wore as he led the team to the 34-28 overtime win.
"Someone stole my game jersey," Brady said after kissing Kraft on the cheek.
"You better look online," Kraft responded.
The NFL, which captured the exchange, shared it on Twitter, posting the video with the caption: "Hey can someone give Tom Brady his jersey back? #SB51."
Police previously classified the case as a possible first-degree felony.
"On 2/05/17, the City of Houston hosted Super Bowl LI in the NRG Stadium. Shortly after winning the game, New England Patriots quarterback Tom Brady noticed his game jersey missing from his locker in the Patriots designated locker room," according to the police report detailing the Feb. 5 incident at NRG Stadium.
Brady, listed as the complainant in the Feb. 6 police report, told reporters the day after the game: "I put it in the bag, and then I came out and it wasn't there anymore. So it's unfortunate because that's a nice piece of memorabilia. So if it shows up on eBay somewhere, someone let me know."
ABC News' Katie Conway contributed to this report.