The post of prime minister was scrapped in 1976 by the then revolutionary leader Fidel Castro. It was reinstated under the rules of a new constitution for the communist-run island passed earlier this year.
Marrero, 56, will take on some of the responsibilities that currently fall to the president.
"The head of government will be the administrative right hand of the president of the republic," the BBC reported on Sunday citing state-run online news outlet Cubadebate.
However, critics say any such changes are purely cosmetic as the Cuban Communist Party and the military remain the only two real decision-making institutions on the island.
Marrero's appointment was ratified unanimously by deputies in the National Assembly on Saturday.
The state newspaper Granma described Marrero as a politician who had emerged "from the base" of the tourism industry, one of Cuba's main sources of foreign exchange.
In 2000 he was made president of the military-run Gaviota tourism group, whose hotels are subject to US sanctions under the Trump administration.
Marrero was named tourism minister in 2004 by Fidel Castro and has since overseen a major boost in tourism to the island.
It is unclear if he will now remain head of the ministry.
Naming him prime minister, Diaz-Canel praised Marrero in particular for his handling of relationships with foreign investors.
He highlighted his "honesty, ability to work, and loyalty to the Communist Party and the revolution".
( With inputs from IANS )