Ankvab, a former pro-Russian businessman who was appointed acting president following the death of previous president Sergei Bagapsh in May, won the election with 54.9% of votes, according to official results published on Saturday (27 August).
The elections were held on 26 August, three years after a brief Russian military intervention which saw Moscow seize control of Georgia's breakaway regions of Abkhazia and South Ossetia.
Russian President Dimitry Medvedev congratulated Ankvab, wishing him "every success" in his new position. Medvedev and Ankvab "confirmed their commitment to further strengthening Russian-Abkhazian relations," the Kremlin said in a statement.
The Georgian Ministry of Foreign Affairs, meanwhile, described the vote as "mockery of international law". All three candidates in the election, including Ankvab, were against any reunification with Georgia.
The election results were rejected by EU foreign policy Chief Catherine Ashton, who reiterated the European Union's "support to the territorial integrity and sovereignty of Georgia, as recognised by international law".
Jerzy Buzek, president of the European Parliament, added: "The European Union does not recognise the constitutional and legal framework within which these elections have taken place."
"Abkhazia is an autonomous region part of Georgia and the European Parliament is committed to the sovereignty and territorial integrity of Georgia."
An agreement brokered by the French EU Presidency in 2008 saw Moscow commit to withdrawing its troops to pre-conflict positions. But the agreement has not been respected, Buzek said.
Earlier, NATO Secretary-General Anders Fogh Rasmussen had issued a statement saying that the military alliance "reiterates its full support for the sovereignty and territorial integrity of Georgia within its internationally recognised borders".
Both Ashton and Buzek emphasised "the importance of the Geneva International Discussions in ensuring the security and stability in the region".
Meanwhile, EU countries approved a proposal to nominate Philippe Lefort, a French diplomat, as the European Union's Special Representative (EUSR) for the South Caucasus and the crisis in Georgia.