Mr Valls said the Socialists were dead and "I will be a candidate for the presidential majority".
Party officials reacted warily, saying he had 24 hours to sign up.
Emmanuel Macron won the presidency on Sunday and his new party has begun picking candidates for the June vote.
The party, which has changed its name from En Marche (On the move) to La République en Marche, intends to have a list of candidates ready for the June vote by Thursday, drawn up from across French politics and civil society.
Mr Valls resigned as prime minister when he stood unsuccessfully in the race to be Socialist presidential candidate and later backed Mr Macron to be president.
However, his approach on Tuesday was not immediately welcomed with open arms.
Macron spokesman Benjamin Griveaux, told French radio that Mr Valls had not yet been registered as a candidate by the party.
"He should have applied like everyone else because the rules are the same for everyone. If you don't put your name forward you can't be selected by En Marche. He's got 24 hours," he said.
Mr Macron won 66.1% of the vote on Sunday, while far-right opponent Marine Le Pen attracted 33.9% of the vote. A quarter of the population abstained in the election and more than 11% either cast blank votes or spoilt their ballot.
Mr Valls's assertion that the Socialists were dead prompted anger from party colleagues.
"I hope for France's sake that Brutus and Judas don't seek En Marche's party nomination," said Socialist MP Alexis Bachelay.
Macron: The days ahead
9 May: Mr Macron will mark the EU's Europe Day, the annual celebration of peace and unity in Europe. In his victory speeches on Sunday he focused on the need for a strong Europe
10 May: Marks France's Slavery Remembrance Day, then in the afternoon attends the funeral of Corinne Erhel, the legislator who collapsed and died while speaking at a Macron rally last Friday. Official election results are published
14 May: President François Hollande formally hands over power to Mr Macron
15 May He will name his choice of prime minister
15-19 May: Mr Macron must finalise candidates for his party in the parliamentary election
11 and 18 June: Parliamentary election held over two rounds. All 577 seats are being contested in a first-past-the-post system