The mystery thriller, which stars Sam Neill, Lost's Jorge Garcia, Parminder Nagra and Big Love actress Sarah Jones, premieres on Watch on March 13.
Alcatraz focuses on an investigation into the sudden disappearance of convicts and guards from the famous prison following its closure in 1963.
Abrams, who serves as executive producer, told Digital Spy that he is "very excited" about the future of Alcatraz, which he described as an "excellent show".
Abrams previously said that he was intrigued by the mystery at the centre of Alcatraz.
"I liked the idea... of the worst of the worst being sent to that place," he said. "What happens if they all disappeared one day, and what happens if they suddenly came back and had not aged a day? The premise from the very beginning is something I knew I would watch."
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