Stepping down from the presidency, Chirac is ending a 40-year career in politics.
He said he was "proud" of his accomplishments, but did not list them.
The 74-year-old offered Sarkozy, who won French presidential elections on May 6, his best wishes.
"I know that the new president Nicolas Sarkozy will be eager to lead our country further down the road of the future.
"And my best wishes go with him on this most demanding and beautiful of missions."
Sarkozy, a firm ally of George Bush, the US president, is set to begin his period in power on Wednesday with a visit to the German capital Berlin and a meeting with Chancellor Angel Merkel.
Chirac founded the neo-Gaullist Rally for the Republic party, today transformed into the Union for a Popular Movement, or UMP, that Sarkozy headed before being elected president.
He is to receive about 6,000 euros ($8,120) a month in retirement pay as a former president.
Chirac is also automatically is entitled to join the Constitutional Council, one of the highest bodies in France, as a former president.
He said he planned to devote himself to campaigning for sustainable development and dialogue between cultures.
One of Chirac's last acts as president was to accept de Villepin's resignation, a spokesman for the president's office said.
The next French prime minister is widely expected to be Francois Fillon, a conservative who take office as early as Thursday morning.
Villepin, a former foreign minister who was fiercely opposed to the Iraq war, was appointed prime minister by Chirac in May 2005 after France rejected the EU constitution in a referendum.
His short time as head of government was marked by riots in ethnically-mixed suburbs, protests over a youth jobs law and accusations that he orchestrated a smear campaign against Sarkozy.