With 58 percent of the two million voters in the deciding round of the Socialist-organised primary backing him, Hamon has a mandate that is also a disavowal of the record of President François Hollande's government.
Hamon quit his post as education minister in 2014 along with other left-wing rebels in protest at the pro-business policies of a government headed by his rival in the primary, Manuel Valls.
The turnout in the second round of the primary was higher than in the first but lower than in the Socialists' first primary, in 2011.And it was dwarfed by the five-million turnout in the mainstream right's first primary, which saw former prime minister François Fillon chosen last month.
Will Socialist MPs back Hamon?
Hamon's victory is one of several results that have shown a polarisation to both the left and the right in Europe and America recently.
Like British Labour leader Jeremy Corbyn, also the beneficiary of a surprise win in a primary last year, Hamon's left-wing stance has gathered enthusiastic support among party sympathisers but is judged unrealistic by many of his own party's MPs.
Just before the deciding round Valls himself said that he could not campaign for Hamon's programme, whose most notable proposal is a universal basic income.
The two also disagree on how Muslims should fit into France's version of secularism.
Valls has let it be known that he will not be present at Hamon's investiture as candidate next Sunday.
Several of the former prime minister's supporters have threatened to switch their loyalties to former economy minister Emmanuel Macron, who was never a Socialist Party member and quit the government launch a bid for the presidency, forming his own party in the process.
But one of Valls's key allies, Philippe Doucet, put their number at 10 or less.
"First of all, we don't know what Emmanuel Macron thinks," he told RTL radio. "And then, when you are a Socialist MP, elected by Socialist voters with Socialist activists, you have to answer to your own activists and voters."
Appeal to hard left
Another problem for Hamon is that several other left-wingers had thrown their hats in the ring before he won the Socialist nomination.
Jean-Luc Mélenchon, who is backed by his own Left Party and the Communist Party, has been showing better in the opinion polls that any Socialist candidate and has ruled out withdrawing from the race, pouring scorn on the Socialists' record in government.
But that was before Hamon's surprise win and the hard-left candidate has recently noted that Hamon's position was "so close to ours".
Green party candidate Yannick Jadot, who represents a party that has lost several of its leading members in the last year and has poor poll ratings, has also said that he is not thinking of withdrawing, although he has hailed Hamon's commitment to the ecology and backed many of his other positions.
Hamon on Sunday said that his first task would be to try to rally the left, although it looks as if he may have his work cut out.
Macron profits from Fillon's misfortunes
The run-up to this election has been as full of surprises as the US presidential election, the Brexit vote and Greece's troubles with eurozone membership.
Fillon came from behind to win of the mainstream right primary on a socially conservative, economically austere ticket.
But he appears to be undergoing a stark reversal of fortunes following allegations that his wife, Penelope, was paid to do nothing or very little from the public coffers.
That should benefit far-right candidate Marine Le Pen, whose National Front did not risk a primary and who the polls show facing Fillon in the presidential decider.
But it also seems to be benefiting Macron, 39, whose image as a new broom who will sweep French politics clean is hardly burnished by the fact that he was a minister in Hollande's government.
He has been accused in a book, L'Enfer de Bercy, of spending 80 percent of his economy ministry's entertainment budget but, as Fillon's supporters ruefully commented on Monday, the allegation does not seem to have done him as much harm as Penelopegate has done their man.
Hamon meets Cazeneuve, Hollande
On Monday afternoon Hamon was to meet Prime Minister Bernard Cazeneuve, who earlier advised Socialist sympathisers not to pick a candidate who criticised the government's record.
Later in the week he is to meet Hollande, who on Sunday evening congratulated the French handball team for winning the world title but not his own party's newly chosen presidential candidate.
Most of the French media have predicted nothing but trouble ahead for Hamon.
But in today's febrile political atmosphere, the French presidential race could have more surprises in store.