Reynolds, at a downtown news conference, announced he would be a candidate to succeed former Democratic Rep. Jesse Jackson Jr. in Illinois' sprawling 2nd Congressional District, which includes portions of Chicago's South Side and suburbs.
Jackson, 47, resigned last week while undergoing treatment for biopolar disorder amid reports he is under federal investigation for alleged misuse of campaign funds. Jackson replaced Reynolds in a special election in 1995.
Flanked by red-and-white campaign signs reading: "re-elect Reynolds" and "Redemption," Reynolds, 60, told reporters his candidacy was not a joke.
"The fact of the matter is, no nobody's perfect," said the Harvard University graduate and former Rhodes scholar. He said voters should "look at the entire history of me."
Reynolds, a self-employed financial consultant who works with African investors in U.S. companies, acknowledged his "mistakes" but said he had paid his debt to society and his convictions "shouldn't be a life sentence."
"I made mistakes," he said. "I want to serve."
He served time in state prison for having sex with a teenage volunteer campaign worker and another 42 months for convictions on federal financial and campaign fraud charges.
As a convicted felon, Reynolds is barred from seeking state office, but he can run for Congress, where he served on the tax-writing House Ways and Means Committee during his two-year term.
In 2001, President Bill Clinton commuted his sentence to time served and he is not required to register as a sex offender, the Chicago Tribune said.