Around the nation, Mr. Jackson’s colleagues in Congress and in his own offices expressed sadness over his departure, but few seemed truly surprised. Mr. Jackson, who was once spoken of as a future candidate for the Senate or for mayor of Chicago or even president, disappeared from public view in June, seeking medical treatment in Minnesota and Arizona.

By this month, some leaders in Chicago, including Mayor Rahm Emanuel, had publicly suggested that Mr. Jackson needed to address his constituents, one way or another. Even on Wednesday, there was no official announcement of the resignation, only the letter. Mr. Jackson’s whereabouts was undisclosed. He did make private phone calls on Wednesday to tell some colleagues of his decision, and several described those talks as sorrowful. “He sounded in so much pain,” Representative Bobby L. Rush of Illinois said.

Still looming is the criminal inquiry into Mr. Jackson’s use of campaign funds.

“I am aware of the ongoing federal investigation into my activities and I am doing my best to address the situation responsibly, cooperate with investigators and accept responsibility for my mistakes, for they are my mistakes and mine alone,” Mr. Jackson wrote in his letter. “None of us is immune from our share of shortcomings or human frailties and I pray that I will be remembered for what I did right.”

While Mr. Jackson did not cite the investigation as a reason for his departure, legal experts said his resignation might help lawyers argue for leniency, given that he has already paid a significant penalty: his job. A statement issued by his lawyers, including Dan K. Webb, a former United States attorney from Chicago, suggested that talks with prosecutors were under way. “We hope to negotiate a fair resolution of the matter, but the process could take several months,” the lawyers said.

Gov. Pat Quinn of Illinois pledged to set a date for a special election swiftly. By law it must take place within 115 days of that date. Already, numerous people appeared to be eyeing the seat. “Every other African-American politician I talk to on the South Side is thinking about running,” said Laura Washington, a political analyst here.