Ms Marin is heading a five-party, centre-left coalition alongside four other parties all headed by women - three of whom are in their early 30s.
The 200-seat Eduskunta parliament approved Ms Marin in a 99-70 vote. The government has a comfortable majority of 117 seats.
The previous youngest world state leader was Oleksiy Honcharuk, who is the current Prime Minister of Ukraine after he was appointed by comedian-turned-president Volodymyr Zelensky in August.
Ms Marin had previously served as the minister for transport and communication since June this year.
Her new finance minister, Katri Kulmuni, is even younger at 32, and only one of her coalition partners is over 35.
'Within four years we won't complete Finland but it can become better...I want to build a society in which every child can become anything and in which every human being can live and grow old with dignity,' Marin wrote on Twitter.
President Sauli Niinisto will formally hand Ms Marin her mandate later on today, after which she will officially become prime minister.
The appointment of Ms Marin and her new government allows her to represent Finland at the European Union summit in Brussels later this week. Finland holds the bloc's rotating presidency until the end of the year.
Finland's government resigned last week after the Centre Party said it had lost confidence in Social Democrat Prime Minister Antti Rinne over his handling of a postal strike.
Ms Marin's coalition cabinet consists of 12 female and 7 male ministers.
Deep divisions remained between the main coalition partners, Marin's Social Democrats and the Centre Party.
Marin will struggle to defend her leftist views against the Centre Party, which wants action to boost Finnish employment to pay for the costly welfare state.
Strikes continued as she took office and populist nationalism looms over its politics..
Kulmuni, chairwoman of the Centre Party which holds the balance of power in parliament, defended her decision to oust the outgoing prime minister Rinne, accusing him of taking the employees' side in recent labour market disputes.
Before his resignation, Rinne defended the publicly-owned postal service's employees in their labour dispute by saying their employment conditions would not be trampled while his government was in office.
'It became sort of an habit to flag in advance in favour of one side, in matters which should be dealt with cool impartiality,' Kulmuni wrote in a long post on Facebook.
Having emerged as Finland's largest party in April elections, the Social Democrats were able to appoint one of their own to the post of prime minister in the Nordic nation of 5.5 million people.
The coalition of the Social Democrats, the Centre Party and three junior partners has said it is committed to the government programme agreed on after the April poll and will continue in Ms Marin's new cabinet.
Ms Marin, who was the number two in the Social Democratic Party, takes over from incumbent Rinne, who stepped down a week ago after key coalition partner the Centre Party withdrew its support, citing lack of trust.
Mr Rinne has said he plans to continue as party leader until a congress next summer.
The youngest ever prime minister of Britain was William Pitt the Younger who got int office aged 24 in 1783.