Castro, 86, was due to step down on Thursday after 10 years in office.
Mr Castro, who was president from 2008 when he took over from his ailing older brother Fidel, will retain considerable clout as he will remain head of the Communist Party until a congress in 2021. After being sworn in to the new post, he promised to "continue the revolution" and noted that his predecessor, Raul Castro, will continue to make essential decisions. The system has one type of Cuban peso worth 1:24 against the dollar for ordinary Cubans, who receive subsidies, and another, the CUC, that is 1:1 for state-run firms, giving those with access to the CUC significant hard currency advantages.
Cubans hope the next government can resurrect one of the world's last Soviet-style centrally planned economies that has failed to improve under limited market reforms by Mr Castro.
We are more anxious about the day to day than politics, said Ricardo Lugone, 28, who earns his living as a private hairdresser, an industry that was state run until Castro relaxed some restrictions after taking over from his brother Fidel in 2008.
The vote on Thursday marked the end of an era for Cuba, making Diaz-Canel the first person outside the Castro family to rule the country in 59 years.
People who know Diaz-Canel as a youth claim he maintained long hair and listened to rock music when he became the first party secretary of Villa Clara province, the capital of which is Santa Clara, giving him a seat on the powerful Central Committee of the Communist Party. Diaz-Canel was born a year after the Cuban revolution.
Eduardo Gamarra, a professor of Latin American politics at Florida International University in Miami, said Diaz-Canel is neither a progressive nor liberalizing politician.
Cuba watchers say the economy hasn't been as weak as it is now since the so-called Special Period that followed the collapse of the Soviet Union in the early 1990s. Cuba's legislature opened the two-day session that is to elect a successor to President Castro.
It has been almost 60 years since Fidel and Raul Castro descended from the Sierra Maestra mountains with a band of communist guerrillas to oust US-backed authoritarian President Fulgencio Batista. He praised both Castro brothers in his speech but singled out Raul, according to USA Today. Relations with Washington had been hostile since soon after Fidel Castro took the island on a sharply leftward path after the revolution. For his part, Chinese Prime Minister Li Keqiang congratulated the new Cuban president and expressed his wishes to boost relationships.
Since then, he has advocated pro-LGBT legislation and anti-discriminatory clauses in the new labour code.
The 57-year-old, who has spent years climbing the party ranks, was named the sole candidate for the presidency..
The first vice president will be Salvador Valdes Mesa, who at 72 is between the two generations. Eleven new members have been proposed, and those put forward for five vice president slots include three women. As Havana's main political ally in the Americas, the socialist regime of Venezuela has significantly cut back subsidized oil shipments in a blow to Cuba's economy. However, many Cubans interviewed by Reuters said they were barely paying attention to the transition.
Reforming the monetary system would be redistributive, creating winners and losers that could unleash political uncertainty.
Change would be good to give opportunities to the opposition, so that there are other parties and freer elections, said Ruben, 51, a musician who did not want to give his full name for fear of reprisals.