Centrist Macron who served in Hollande's government, won a emphatic victory over the far-right's Marine Le Pen in Sunday's election.
On Monday, Macron resigned as the leader of En Marche! political movement, with Catherine Barbaroux appointed as an interim leader.
Mr Valls said that "I will be a candidate in the presidential majority and I wish to join up to his movement, the Republic on the Move".
According to Richard Ferrand, the En Marche! campaign manager, the organization has so far managed to attract 285,000 members. That will require putting together a slate of candidates affiliated or allied with his party for the June elections for the National Assembly and getting them elected in the face of opposition from the two big parties - the Socialists and the Republicans - that were shut out of the second round as well as from the Front National.
Macron, 39, will enter the Elysée, the presidential office and residence, on May 14 as the youngest president in French history.
"His large victory confirms that a very large majority of our citizens wanted to assemble around the values of the Republic and mark their attachment to the European Union as well as to the openness of France in the world", Hollande said in a statement.
Putin welcomed Macron's main rival, the National Front's Le Pen, called "Our Marine" in some state media, on her first public visit to the Kremlin in April.
"I will fight the divisions that undermine France", he added in a nod to the 11 million votes Le Pen received, a record for the far-right leader.
French Economy and Industry minister Emmanuel Macron is pictured during a press conference following a meeting amid a crisis in France's agricultural sector in Paris on February 8, 2016. U.S. President Donald Trump called to congratulate Macron, while on the Kremlin website, Russian President Vladimir Putin urged Macron to "overcome mutual mistrust and unite to ensure worldwide stability and security".More news: Under Trump, daylight re-emerges in US-Israel relationship
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An estimation by research firm Elabe for BFMTV show that Macron won the presidential race with 65.9 percent of votes, while Le Pen scored 34.1 percent.
Some urged him to lay out a clear quid pro quo on Europe, explaining reforms he would do as French president, what Germany could deliver in response, and areas where the two countries should pursue common initiatives, sources in his team said.
Macron, by contrast, embraced globalization, winning an unusually high-profile endorsement last week from former President Barack Obama.
"The Prime Minister warmly congratulates President-elect Macron on his election success".
European Commission chief Jean-Claude Juncker wrote on Twitter that he was "happy that the French chose a European future". "In these conditions it is especially important to overcome mutual mistrust and unite efforts to ensure worldwide stability and security".
European Council President Donald Tusk also congratulated Macron, saying the French have chosen "liberty, equality, and fraternity".
Earlier, Le Pen told supporters she had called to congratulate Macron after exit estimates projected her heavy defeat.
Though Trump never endorsed Le Pen, in an interview to an American news agency he did say that he thought the attack would "probably help" her.