Under the Science Without Borders programme, the Brazilian government will provide 75,000 scholarships for promising students to study overseas over the next four years.
The first 1,500 students have already been selected, and the next round is for a further 12,500 scholarships. Successful students will take up the fully funded places at universities in the US, the UK, Germany, Italy and France starting in 2012.
Launched in July, the scholarship programme aims to address the expanding economy's shortage of chemists, physicists, computer scientists and engineers.
It includes funding for 34,000 doctoral students, although most places would be for undergraduates and run for one year.
Brazilian ministers have challenged business to fund an additional 26,000 scholarships.
The government is also looking to attract foreign scientists to Brazil by funding 390 three-year grants for visiting researchers. In addition it is offering posts for 860 outstanding young researchers.
"With strong growth, economic stability, democracy and increasing investments in research, Brazil has become attractive for scientists," said Aloizio Mercadante, minister of science, technology and innovation.
In June, 13 UK vice-chancellors, including Sir Steve Smith, then president of Universities UK, accompanied David Willetts, the universities and science minister, to Brazil on a trade mission to recruit a reported 10,000 students.
In all, there are 238 foreign universities involved in the scholarship scheme, which were selected on the basis of rankings, including the Times Higher Education World University Rankings.
Announcing the latest round of applications, which closes on 15 January, Brazilian president Dilma Rousseff said: "We will need in the coming years men and women very well prepared and trained to ensure an increase in competitiveness of our economy and our country through science and innovation."