Obama won the presidency last week over Republican John McCain.
Under state law, Democratic Gov. Rod Blagojevich will name Obama's replacement for the remaining two years of his term.
Blagojevich has said he expects to make a decision by year's end, and has ruled out appointing himself. Obama, elected in 2004, is the only black senator.
His resignation reduces the Democratic majority to a bare minimum for the post-election session that begins next week. The party retains control as long as Independent Sen. Joseph Lieberman of Connecticut sides with them.
Some Democrats favor punishing Lieberman, who endorsed McCain, for his speech at the Republican National Convention this summer and other critical remarks about Obama. Obama has told Senate Majority Leader Harry Reid he is not interested in seeing Democrats drive Lieberman from the Democratic caucus.
Blagojevich's appointee would serve until the next national election in 2010.
Obama has made clear he's deferring to the governor, saying last week: "This is the governor's decision; it is not my decision."
However, Obama also said his replacement should be "somebody who is capable; somebody who is passionate about helping working families in Illinois meet their dreams."
Potential candidates to replace Obama include Rep. Jesse Jackson Jr., Rep. Jan Schakowsky, Illinois Senate President Emil Jones and Illinois Attorney General Lisa Madigan.
On Tuesday, Obama appeared with another possible replacement, Iraq war veteran Tammy Duckworth, to commemorate Veterans Day. She is a former congressional candidate and head of the Illinois Department of Veterans' Affairs.
A day later, Obama friend and adviser Valerie Jarrett made it known that she's not interested in the Senate seat.
Blagojevich has said he wants to name Obama's replacement by Christmas. Potential successors said Thursday they had heard nothing from the governor to indicate that he has changed plans or intends to make a decision soon.
Duckworth said the governor's office hadn't contacted her to discuss the position or a timetable. U.S. Rep. Danny Davis said the same, although he predicted Blagojevich wouldn't let the decision wait until Christmas.
"My sense is that the governor will probably not drag this out too long," said Davis, D-Ill.
Obama's aides say his Senate office will remain open for a while so that staffers can archive Senate documents for Obama's future presidential library and contact constituents. It will close some time within the 60 days after the resignation becomes effective Sunday.
Vice President-elect Joe Biden also is expected to resign his seat representing Delaware at some point between now and the Jan.
20 inauguration. Democratic Gov. Ruth Ann Minner presumably would pick the successor.
Several Democrats have said Biden's son, Delaware Attorney General Beau Biden, is interested in succeeding his father in the Senate. He is on a yearlong deployment to Iraq with his National Guard unit. As a result, Democrats have discussed a plan under which an interim successor would be named and would step aside in 2010 so the younger Biden could run in a special election to fill out the term.
Democrats say the vice president-elect has told associates he intends to be sworn into his new Senate term in early January, and resign his seat before the inauguration.
-- Associated Press writers Nedra Pickler in Washington and Christopher Wills from Springfield, Ill., contributed to this report.
