Valérie, who works as a journalist for Paris Match magazine, spent eight days in the Pitié-Salpêtrière hospital before moving to the presidential home of Pavillon de la Lanterne, near Versailles.
"Thank you from the bottom of my heart to all those who sent supportive or get well messages via twitter, SMS or email," tweeted Valérie. "Very touched."
Valérie's 16-year-old son Léonard was happy to be reunited with his mother.
"Finally with my mother!" He tweeted. "I'm glad to be reunited with her. She left hospital this afternoon."
President Hollande has yet to make an official comment on the rumours of his affair, but has said that he will clarify if Valérie will continue to act as France's first lady before he makes a state visit to the United States on 11 February.
Some political watchers commented that it was telling President Hollande had not visited his partner in hospital, although Valérie was quick to dismiss such rumours.
The 48-year-old called a French radio station to say that her doctors had told Hollande he could not visit her so he had sent her flowers and chocolates instead.
Valérie was admitted to hospital on 10 January, with friends saying that she had taken "one pill too many" after hearing the rumours of her partner's affair.
"The doctors say she needs more rest and they will decide when she will be able to leave," a spokesperson at the Elysée Palace told Reuters last week. "She needs some peace."
Some critics have accused Valérie of trying to win public sympathy, and use her health to put pressure on the president to leave his 41-year-old mistress adding that she was reluctant to give up her life in the presidential palace and the luxuries it afforded her.