Nearly 3,000 miles separate the capitals of Haiti and Brazil but that hasn’t prevented Haitians from making their way to Latin America’s largest country to get work.

Some 2,400 illegal Haitians have even crowded into remote western Amazon towns where they’re living in precarious conditions, often following a route that takes them from Haiti to the Dominican Republic to Panama to Lima, then on to Iquitos, Peru, where they catch a boat to the Brazilian outposts on the banks of the Amazon River.

Now, the Brazilian National Immigration Council has begun a program to not only grant visas to Haitians who have already crossed Brazil’s borders illegally but also to allow about 100 Haitians per month to enter Brazil to work legally. At its embassy in Port-au-Prince, Brazil plans to issue 1,200 permanent visas annually to Haitians whose lives were torn apart by the social and economic upheavals of Haiti’s 2010 earthquake.

One thing that Brazil needs as the 2014 World Cup and the 2016 Olympic Games in Rio de Janeiro approach is workers. Unemployment is at historic lows, labor shortages have cropped up around the country and the word has filtered to Haiti.Despite the Haitians’ circuitous route, “they were definitely aiming for Brazil. They have the idea that in Brazil they will find jobs and a better life,’’ said Alessandra Vilas Boas, director of communications for the Doctors Without Borders program in Brazil. The humanitarian organization has been aiding the displaced Haitians.

Some follow a portion of a well-established route that small-scale merchants take to Panama to buy cheap products. Another smuggling route takes Haitians via the Dominican Republic, Ecuador and Peru, said Igor Kipman, Brazil’s ambassador to Haiti.

The exodus comes as Haitians’ frustration is mounting over the plodding pace of job creation at home, and they continue to take to the sea in search of better opportunities. In the first 3 ½ months of the fiscal year that began Oct. 1, U.S. Coast Guard statistics show that interdictions of Haitians at sea have increased by 250 to 488 compared to the same time a year ago.

The special work program will allow Haitians to remain in Brazil for five years, and does not require participants to show proof of education and labor skills nor that a job is waiting for them — unlike other Brazilian work visa programs, Paulo Sérgio de Almeida, president of the National Immigration Council, said in an email..

If they want to remain in Brazil permanently, the Haitian immigrants will be required to show proof of employment before the end of the five-year period.

“We hope that Haiti will start to improve job conditions for the Haitian population. As Haiti establishes a pattern of sustainable development and economic growth, Haitians will no longer feel the need to seek out a better life abroad,’’ said Antonio Patriota, Brazil’s minister of foreign relations.

Besides leading the largest contingent of U.N. peacekeepers in Haiti, Brazil was one of the first donors to contribute to a post-earthquake reconstruction fund. It also has made social investments, working in the Haitian slums and financing the construction of community clinics, and is currently seeking partners to help build a $150 million hydroelectric dam on the Artibonite River.