The Cuban government welcomed Morales' election as an important triumph over US influence in the region.
Castro said: "I think that it has moved the world. It's something extraordinary, something historic. The map is changing."
Castro, 79, sent his private plane to bring Morales to Havana, on his first visit abroad since winning Bolivia's 18 December presidential vote.
Morales, who has never hidden his admiration for Cuba's revolution, said he felt "joy, great emotion to be here".
Morales referred to Castro as "el comandante" and said his trip was a gesture of "friendship with the Cuban people".
Morales' visit to Cuba underlines the political loyalties of the leftist leader, who pledged to join Castro's "anti-imperialist struggle" in a message to the Cuban people the day after his election.
Castro said Morales' election was "something extraordinary" that had "rocked the world". Morales will be the first indigenous president in Bolivia, which has a majority of ethnic Aymara and Quechua peoples.
"Our brother Evo possesses all the necessary qualities needed to lead his country."
Despite US efforts to isolate Cuba, Castro enjoys very close ties to Hugo Chavez, Venezuela's leftist president.
"Our brother Evo possesses all the necessary qualities needed to lead his country"
Left-leaning governments have come to power elsewhere in the region, from Argentina and Uruguay to Chile and Brazil.
Castro said "during our discussion we were in touch with Chavez," but he did not offer further details.
A week ago, Chavez, referring to Morales' win, said "(US) threats have already begun. From here on in, we are demanding that the immoral imperialist US government respect the holy sovereignty of Bolivia and the government elected by Bolivia."
As an activist for coca farmers in Bolivia, Morales cultivated friendly ties with Castro for years and has pledged to support Chavez's effort to defeat a US-proposed free trade area.
During his campaign, Morales described himself as Washington's "nightmare".
Evo Morales (L) is Bolivia's first
Morales has struck a more moderate tone since his election, promising Bolivia's business leaders that he will create a climate favourable for foreign investment and jobs, and will not "expropriate or confiscate any assets".
Morales won the presidency with nearly 54% of the vote - the most support for any president since democracy was restored to Bolivia two decades ago.
Morales has vowed to nationalise Bolivia's large natural gas industry and end the US-sponsored coca eradication programme that he says has hurt farmers and failed to curb drug trafficking.
Castro and Morales signed a co-operation agreement late on Friday that would boost Cuba's medical and educational assistance to Bolivia.
Morales has described himself as
Among the poorest and least developed countries in Latin America, Bolivia none the less has a literacy rate of more than 87%.
On 3 January, Morales will embark on an extensive international tour, including visits to Spain, France, Belgium, South Africa, China and Brazil.
Morales has invited Castro to his inauguration ceremonies on 22 January.