Burris, a Democrat, is not seeking a full term.
Hoffman, a 42-year-old former federal prosecutor, joins a Democratic primary field that's likely to include two others. First-term State Treasurer Alexi Giannoulias has already announced his candidacy and Chicago Urban League President Cheryle Jackson is expected to formally enter the race next month.
Republican Congressman Mark Kirk has also announced his candidacy.
Hoffman's announcement was released on hoffmanforillinois.com