McDormand collected the award for Best Actress at the Hollywood ceremony on Sunday night for her role in Three Billboards Outside Ebbing, Missouri.
Bryant's boasting on Sunday night caught the attention of a photographer who did not recognize him as a victor at the ceremony and began following him, police said.
The actress clutched her award through the post-win press conferences and took it with her to the annual Governors Ball celebration.
He was convicted of receiving stolen property in Los Angeles County in 2004 and sentenced to 24 days in jail and three months of probation, online court records show.
Her publicist said she celebrated being "happily reunited" with the award with a double cheeseburger from California's In-N-Out Burger chain.
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Gwala has represented South Africa at global competitions in Chicago in 2015 and in the Netherlands previous year . The three attackers sawed into Gwala's right calf and damaged muscle, nerves and bone, Jackson said.
While Rockwell won the Oscar for his performance, it's very likely that even his character, the bumbling Dickson, would have been able to arrest the man who briefly stole Frances McDormand's Oscar for Best Actress.
It was not immediately clear in what capacity he was attending the event, but police said he had a ticket. He was located with the Oscar pre-engraved with Frances McDormand's name.
Bryant is expected to be arraigned in a downtown Los Angeles courtroom on Wednesday.
Police said the Los Angeles resident handed the gold-plated bronze statuette back without a struggle and was arrested. His social media accounts also include photos of him at shows including the Emmys, Screen Actors Guild Awards and MTV Video Music Awards.
In Three Billboards, McDormand plays a mother who challenges authorities over finding the culprit for the rape and murder of her daughter.
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Is David De Gea the only world-class player at Manchester United? Without Zaha, Roy Hodgson will lean on Christian Benteke . Manchester United are not in action until Monday evening when they take on Crystal Palace at Selhurst Park (8pm).
It's the second time Frances has bagged an Academy Award, 21 years after her first for "Fargo".
"Security at the Governors Ball are looking for this guy, who grabbed Frances McDormand's Oscar and ran out with it", said New York Times writer Cara Buckley, who was at the event and live-tweeted the drama.
"Look it, baby. My team got this tonight".
As he spun around in a circle, Bryant solicited congratulations from those around him.
"You know what, I can't believe I got this".
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However, we just watched Justino soundly outbox a world-class boxer in Holly Holm , who also supplements her handcraft with kicks. I like it and I become a better fighter when I know it's a big event or an all eyes on me type thing.