The panels are expected to provide 40 to 60 percent of the island's electricity and reduce the need for two aging diesel generators.
Officials say the generators pollute the environment and cost $700,000 a year to fuel and maintain.
The panels are expected to go up in the spring with money from the federal stimulus program. Cost estimates are not being released.
Alcatraz was taken over by the Bureau of Prisons in 1934 and housed some of America's most notorious inmates, including Al Capone.
The island, also known as "The Rock," is today a popular tourist destination.