"I did not break the law and I never ever thought that I was breaking the law," said Edwards, accompanied by his oldest daughter, Cate.
The charges concern hundreds of thousands of dollars provided by two wealthy donors that Edwards allegedly used to shelter his mistress, Rielle Hunter.
Edwards acknowledged making mistakes, but said they weren't crimes.
"There's no question that I've done wrong and I take full responsibility for having done wrong and I will regret for the rest of my life the pain and the harm that I have caused to others," he said outside the courtroom.
Edwards did not have to post bond but surrendered his passport and was ordered to stay in the continental United States. He declined to answer questions from reporters.
Earlier, lead defense attorney Greg Craig told reporters that "no one" has ever been charged "with the claims brought against senator Edwards."
A youthful, silver-tongued trial lawyer elected senator from North Carolina, Edwards sought the Democratic Party presidential nomination in 2004 and 2008.
He became Democrat John Kerry's running mate in 2004, but they lost to Republican George W. Bush, who was re-elected. Four years later, Barack Obama won the Democratic nomination and presidency.
The indictment marks a stunning fall. Edwards was wealthy, had a model family after marrying his college sweetheart and fathering four children, and had seemed destined to be a leading Democratic voice.
His wife Elizabeth, an attorney and campaigner, had inspired America when she revealed she was battling breast cancer. She died in December after having secretly grappled for years with her husband's infidelity.
During his 2008 run, Edwards allegedly accepted "more than $900,000 in an effort to conceal from the public facts that he believed would harm his candidacy," US Assistant Attorney General Lanny Breuer said in a statement.
"As this indictment shows, we will not permit candidates for high office to abuse their special ability to access the coffers of their political supporters to circumvent our election laws."
The case relies heavily on Andrew Young, a former close aide to Edwards who initially claimed to be the baby's father so the politician could continue his 2008 White House race.
Young later wrote a tell-all book about the affair in which he detailed an elaborate cover-up. He also testified before a North Carolina grand jury.
Edwards admitted to the affair in August 2008, after his campaign ended, but did not recognize he had fathered the child until January 2010.
His wife was informed of the affair in 2006 while she was being treated for cancer.
She recovered and played a central role in his 2008 presidential run, but died at the age of 61 after the cancer resurfaced.
Much of the case hinges on whether the money used in the cover-up came from personal gifts or illegal campaign donations concealed from election authorities.
The Edwards defense team includes Scott Thomas, a former longtime employee of the Federal Election Commission, the campaign watchdog agency. He claimed the government's argument is an "erroneous reading of the law."
Edwards faces one count of conspiracy to violate the federal campaign finance laws and lying about expenses; four counts of accepting and receiving illegal campaign contributions from two donors in 2007 and 2008; and one count of hiding those illegal donations from authorities.
Each of those charges carries a prison sentence of up to five years and a $250,000 fine.
The final count alleges Edwards "knowingly and willingly falsified, concealed, and covered up by trick, scheme and device material fact" hundreds of thousands of dollars in contributions.