The DGAE electoral authority posted provisional results on Monday showing Pedro Pires had won with nearly 50.8% of the votes in Sunday's poll, compared with 49.2% for Carlos Veiga, the former premier.
Votes had been counted from nearly all of the polling tables.
Although the final result still had to be officially declared, supporters of Pires celebrated in the streets of the capital, Praia.
The preliminary results showed Pires, 71, the victor with 84,793 votes against 82,293 for Veiga, an advantage of 2500 votes for the former guerrilla commander who helped Cape Verde win independence from Portugal in 1975.
Sunday's poll was a rematch of the close-fought presidential election five years ago when Pires beat former premier Veiga by only 12 votes.
The two men have dominated Cape Verde's politics since independence.
The DGAE estimated turnout in Sunday's vote at about 54%.
Veiga, 56, a lawyer who headed the first democratically elected government in 1991 after the African Party for the Independence of Cape Verde (PAICV) gave up one-party rule, represents the Movement for Democracy (MpD), the main opposition party.
Pires had been counting on an electoral boost from last month's parliamentary elections in which the PAICV retained its parliamentary majority. It won 41 seats in the 72-member National Assembly against the MpD's 29 seats.
Both candidates had promised to promote faster growth and investment in Cape Verde, which is trying to cash in on growing tourism development and as a strategic air and sea transport hub 500km off the African continent.