“Guilty, Your Honor — I misled the American people,” Mr. Jackson said when asked whether he would accept the plea deal. Mr. Jackson’s father, the Rev. Jesse L. Jackson, his mother and several brothers and sisters accompanied him to the hearing.

Mr. Jackson’s wife, Sandi, also accompanied him, and later in the day she pleaded guilty to a charge that she filed false income tax statements during the time that Mr. Jackson was dipping into his campaign treasury. Prosecutors said they would seek to have her sentenced to 18 to 24 months.

Mr. Jackson’s plea was yet another chapter in the downward spiral of his career. Elected to Congress in 1995 at the age of 30 from a district that includes part of the South Side of Chicago, Mr. Jackson was once one of the most prominent young black politicians in the country, working on issues related to health care and education for the poor.

But as the federal authorities investigated Gov. Rod R. Blagojevich of Illinois over his efforts to sell the Senate seat that President Obama vacated in 2008, they uncovered evidence that one of Mr. Jackson’s friends had offered to make a contribution to Mr. Blagojevich’s campaign in exchange for the seat. Since then, Mr. Jackson, who has said he had no knowledge of the offer, has been dogged by questions about his ethics.

Last summer, Mr. Jackson took a medical leave from Congress and was later treated for bipolar disorder. After winning re-election in November, he resigned, citing his health and the federal investigation into his use of campaign money.