Brady and running mate Jason Plummer made their announcement in Bloomington, Brady's hometown.
Quinn held a vote margin of less than 20,000 votes, making this the closest election since 1982 when then-Republican Gov. James Thompson defeated former Sen. Adlai Stevenson III by 5,083 votes.
Brady said he called Quinn shortly before the news conference and "congratulated him on his victory." But Brady took the opportunity to repeat some of his favorite campaign themes, criticizing Quinn for plans to hike the state income tax and for failing to turn the state's economy around.
"There's nothing more important to Illinois families than an economy that provides jobs," Brady said.
Quinn, who was elevated from lieutenant governor to governor after Rod Blagojevich was impeached following his indictment on federal corruption charges, discussed his agenda in general terms Thursday, saying, "We have a lot of work to do," the Chicago Tribune reported.
"I have to do my job right now as governor," Quinn said. "I have work to do. I know the people of Illinois want to make sure we get our economy back in stride, and that's what I focus on night and day."