Marin, who is currently the Minister of Transport and Communications, narrowly won over Antti Lindtman, the 37-year-old chairman of the Social Democratic Parliamentary Group, in a vote of 32-29 on Sunday.
She was picked on Sunday by her Social Democratic Party (SDP) to take charge after Prime Minister Antti Rinne quit, the BBC reported.
Rinne stepped down after losing the confidence of a coalition member over his handling of a postal strike.
She is expected to be sworn in this week and will lead a centre-left coalition of five parties all headed by women.
When she takes office, Marin will be the world's youngest sitting Prime Minister. New Zealand Prime Minister Jacinda Ardern is 39, while Ukrainian premier Oleksiy Honcharuk is 35.
Addressing the media on Sunday, Marin said: "We have a lot of work to do to rebuild trust."
She brushed away questions about her age, saying: "I have never thought about my age or gender, I think of the reasons I got into politics and those things for which we have won the trust of the electorate."
Marin will be the third-ever female Prime Minister in the Nordic country.
The Social Democrats emerged as the largest party in elections held in April, and so can appoint the Prime Minister who leads the coalition government, the BBC said.
Marin has been the Minister of Transport and Communications since June. She is also SDP deputy chair, who led the party during Rinne's extended sick leave last winter.
Marin is also a member of parliament.
She became nationally known first in the municipal political scene in Tampere, the second largest town in Finland. She was the chairperson of the City Council of Tampere from 2013 to 2017.
Marin has a Master's degree in Administrative Sciences in Tampere University.
( With inputs from IANS )