Jerome Cahuzac had committed crimes of "extraordinary" seriousness, a court in Paris said, and sentenced him to three years in prison.
Cahuzac, 64, resigned in 2013 after it emerged he had held an undeclared Swiss bank account and then lied about it.
The affair was an embarrassment to Mr Hollande and caused public outrage.
Mr Hollande had made fighting tax evasion among the wealthy a priority for his Socialist administration. He subsequently ordered his ministers to disclose their personal wealth.
Cahuzac's ex-wife, Patricia Menard, was also jailed for two years for tax fraud.
Cahuzac, a successful cosmetic surgeon who specialised in hair transplants, was appointed budget minister by Mr Hollande in 2012.
He gained a reputation as a vocal crusader against the use of overseas tax havens by the wealthy.
When an investigative website, Mediapart, reported that he had kept an undeclared Swiss bank account until 2010, he denied it furiously.
But shortly after an investigation was opened in early 2013, he admitted having the account, which contained about €600,000 (£460,000; $647,000).
He apologised for hiding the money and said he had been "caught in a spiral of lies".
The court also fined the Geneva bank Reyl €1.8m for keeping Cahuzac's account secret. Banker Francois Reyl was fined €375,000 and given a one-year suspended prison term.
The trial revealed that, in the 1990s, Cahuzac and Menard had moved profits offshore from their lucrative hair transplant business.
They had about €3.5m in secret accounts, including the Swiss one. Menard kept €2.7m in an Isle of Man account, while about €240,000 was paid into accounts belonging to Cahuzac's mother.
A former French budget minister appointed by President Francois Hollande to tackle tax evasion has been jailed for tax fraud.