The 27-year-old mentee of Mrs Le Pen won an internal party vote with 85% support, marking a symbolic changing of the guard at the resurgent National Rally party.
He is the first person to lead the party who does not have the Le Pen name, since it was founded half a century ago.
The National Rally is seeking to capitalise on its recent breakthrough in France's legislative election and growing support for far-right parties in Europe, notably in neighbouring Italy.
It is also facing broad public anger over a racist comment made this week by a National Rally member. Parliament was suspended on Thursday after a black MP was told to “go back to Africa”.
Marine Le Pen is still expected to wield significant power in the party's leadership and run again for France's presidency in 2027.
She says she stepped aside to focus on leading the party's 89 lawmakers in France's National Assembly.
On Saturday, she hugged Mr Bardella to broad applause after the results were announced at a party congress on Paris' Left Bank, and both raised their arms in victory.
Ms Le Pen said Mr Bardella's main challenge will be pursuing the party "road-map" of taking power in France.
"We are going to win," supporters chanted.
Anti-racism activists, union leaders and politicians protested nearby Saturday against the National Rally, denouncing what many see as a creeping acceptance of its xenophobic views.
Yeliz Alkac, 30, told news agency the Associated Press that she was demonstrating to support people who face persistent racism in France. She described shock and dismay that the racist remark toward a black lawmaker in parliament was seen as "normal" by some in France.
"The fact that the National Rally has 89 lawmakers at the National Assembly is a strong signal. It should be a warning about how the extreme right is going strong," she said.
In his speech, Mr Bardella defended the National Rally legislator who was suspended over the remark, calling him a victim of a "manhunt".
Mr Bardella described his family's Italian immigrant roots and pride at becoming French, but made it clear that not all foreigners are welcome.
"France shouldn't be the world's hotel," he said, calling for "drastic" limits on immigration.
He welcomed a representative of Italian Premier Giorgia Meloni's far-right party who came to the congress, calling for a "rapprochement" of similar forces in Europe.
Mr Bardella had been the interim president of the National Rally since Ms Le Pen entered the presidential race last year.
He beat party heavyweight Louis Aliot, 53, who had argued that the National Rally needs to reshape itself to be more palatable to the mainstream right.
"Bardella's election feels like a fresh push," said party member Marie Audinette, 23. "He embodies the youth."
Ms Audinette, who grew up in a working-class neighbourhood in Bordeaux, said that her country "was perishing," citing deteriorating public services that struggled to cope with the Covid-19 pandemic. She also described "a clear change of population" in Bordeaux.
Some far-right supporters in France increasingly refer to the false "great replacement" conspiracy theory that the populations of Western countries are being overrun by non-white, non-Christian immigrants.
The claim, propagated by white supremacists, has inspired deadly attacks.
Ms Le Pen lost to French President Emmanuel Macron on her third presidential bid in April but earned her highest score yet. Two months later, her party won its most seats to date in the lower house of parliament.
Ms Le Pen has worked to remove the stigma of racism and antisemitism that clung to her party. She has notably distanced herself from her now-ostracised father Jean-Marie Le Pen, who co-founded the party then called the National Front and has been repeatedly convicted for hate speech.