Officials say that Brown will make the announcement Friday during a picnic at Prince George's Community College.
The lieutenant governor is also expected to make stops in Frederick, Montgomery County and Baltimore on Saturday.
Brown, a Democrat, has served as the lieutenant governor of the state since 2006 alongside of Gov. Martin O'Malley.
Prior to assuming the post of lieutenant governor, Brown represented Prince George's County for two terms in the Maryland House of Delegates, rising to the position of majority whip.
If elected, he would be Maryland's first African-American governor.
A colonel in the United States Army Reserves, Brown is the nation's highest-ranking elected official to have served a tour of duty in Iraq.