Mark Basseley Youssef will serve the sentence in federal prison after he admitted four allegations of using false identities, violating the terms of his probation for a bank fraud conviction in 2010.
The 55-year-old was identified as the main man behind the film, Innocence of Muslims, which triggered a wave of protests in September and was initially blamed for an attack which killed the US ambassador to Libya.
In February 2009, a federal indictment accused Youssef and others of fraudulently obtaining the identities and social security numbers of customers at several Wells Fargo branches in California and withdrawing $860 from them.
He was arrested in September for eight probation violations.
At a hearing last month he denied all counts, but on Wednesday he admitted to four, in return for the other four being set aside.
US District Court judge Christina Snyder said Youssef, who has already spent five weeks in custody, must spend 12 months behind bars, followed by four years of supervised release.
Youssef was previously listed as Nakoula Basseley Nakoula, and known as Sam Bacile when the protests about the video emerged.
The amateurish film depicting the Prophet Mohammad as a thuggish deviant offended many Muslims, and sparked a wave of anti-US protests that cost several lives and saw mobs set western missions, schools and businesses ablaze.
It was also linked to the September 11 attack on the US consulate in Benghazi in which US ambassador to Libya Chris Stevens and three other Americans were killed.