The court said Mr Rajoelina secured 59% of the votes cast, declaring him elected for a third term.
It dismissed complaints by the opposition over the credibility of the vote, which recorded a low turnout of 46%.
Most opposition parties boycotted the election.
"Andry Rajoelina is elected as the president of the republic of Madagascar and is taking his functions as soon as the swearing [is done]," Florent Rakotoarisoa, the head of the Constitutional Court was quoted by the Reuters news agency as saying.
Ten out of 13 presidential contenders had withdrawn their candidacies but their names remained on the ballot.
They raised concerns about the credibility of the election and asked their supporters not to vote, hence the low turnout considered to be the lowest in the island country's history.
They also denounced Mr Rajoelina's bid for a third term and the validity of his candidacy, given his dual French nationality.
The Constitutional Court however earlier rejected their bid to annul Mr Rajoelina's bit for a new term.
Mr Rajoelina defeated his two closest rivals, Siteny Randrianasoloniaiko and ex-President Marc Ravalomanana, who got 14% and 12% of the vote respectively.
The vote was preceded by weeks of demonstrations and clashes with police, with the opposition accusing Mr Rajoelina of having created unfair electoral conditions.
Mr Rajoelina dismissed the allegations.
The United States and the European Union have led international calls for the president to engage in talks and carry out electoral reforms.