"It would be a high honor to follow the footsteps of Sheriff Mike Hennessey, who is arguably one of the most successful sheriffs in recent history, not just in San Francisco but nationally," Mirkarimi said.
Hennessey, who has been sheriff for the past 31 years, made the announcement Friday in a memo sent out to the entire department, sheriff's spokeswoman Eileen Hirst said.
Mirkarimi said that if elected, he will build on Hennessey's legacy, particularly when it comes to programs to reduce San Francisco's recidivism rate, which is among the highest in the state.
A report released by the California Department of Corrections and Rehabilitation in November 2010 found that 78.3 percent of San Francisco's inmates were arrested or convicted again after release from prison, the third-highest rate in the state.
Mirkarimi said the high recidivism rate "is not just on the shoulders of the sheriff, but the collective shoulders of all criminal investigation departments."
Prior to Mirkarimi's election as supervisor in 2004, he worked for nearly nine years in the San Francisco District Attorney's Office as an investigator specializing in economic and environmental crimes.
He is the chairman of the board's public safety committee and is also a graduate of the San Francisco Police Academy, where he was class president.
Mirkarimi said that given his background, he would be "a very solid fit" for the sheriff's job.
If Mirkarimi is elected in November, the mayor would appoint his replacement as supervisor for the rest of his term, which ends in January 2013.