Bujar Nishani's name was put forward after the ruling coalition's previous candidate, Artan Hoxha, pulled out for unclear reasons. The opposition complained it was not properly consulted on the candidates for the largely ceremonial role.
Nishani, 45, won 73 votes in the 140-seat parliament. Three previous ballots had failed to meet the constitutional requirement for at least 84 votes for a new president. But subsequent votes only require at least 71 votes.
Opposition Socialist Party lawmakers were present Monday but did not take part in the vote. Their leader, Edi Rama, said Nishani's unilateral nomination by the ruling Democrats undermines the country's goal of joining the European Union. Both Nishani and Hoxha were presented by the government without the support of the opposition.
"I do confirm that the majority's candidate withdrew from the race. But the majority is determined to give the country a president. The next candidate will be (Bujar) Nishani," governing Democratic Party lawmaker Astrit Patozi told reporters.
Rama criticized Nishani's candidacy, saying it was a harsh blow to the country's road toward membership in the European Union.
"It is unbelievable that a minister turns into a president ... at this historic, delicate moment," said Rama.
Albania has applied for EU candidate status. It has been turned down twice by Brussels, but hopes for a positive response this autumn.
The presidential election process is considered a test in Albania's road to integration. There has been intensive international pressure for a president with multi-party support, with Western ambassadors holding daily meetings with Albanian political leaders.
U.S. Ambassador Alexander Arvizu had been in parliament to watch the previous three votes but was not there during Monday's ballot.
Late evening Sunday talks between the two main opposing political groups failed to reach an agreement on a presidential candidate.
Albania's president has largely ceremonial powers, but he also nominates the prosecutor general, the head of secret intelligence police, and judges and prosecutors.
OSCE Ambassador Eugen Wollfarth congratulated Nishani after his election, praising the interior minister's work on maintaining the rule of law in Albania.
"I am confident that his profound knowledge and broad experience will allow him to serve his country in the most constructive way," said Wollfarth.
Nishani will replace President Bamir Topi, whose five-year term ends July 24. He had decided not to seek a second term.
Nishani, who will be post-communist Albania's sixth president, also has served as justice and interior minister before. He graduated from a military academy in Albania and also has done post-graduate work in United States and Europe.