Hollande will also travel to the country to attend the inauguration of president-elect Ibrahim Boubacar Keita, a source in Hollande's office said.
In a statement, Hollande said the election had been "remarkably transparent" and well organised.
It said he had telephoned Keita to congratulate him on his victory and "assured him that France will stand by Mali".
"What has happened since the French intervention... up to the election of a new Malian president is a success for peace and democracy," Hollande said.
"But now everything must be done to ensure the success of the end of the transition, dialogue and Mali's development."
France sent troops to Mali in January to block a feared advance on the capital Bamako from the north by Islamist fighters, ousting the rebels from their northern strongholds in a lightning advance.
Hollande was hailed as a hero when he visited the former French colony in February and the source in his office said he would return for Keita's inauguration, expected in September.