The electoral commission said that Michel, 71, had won the second round of the election by just 193 votes -- with 50.15 per cent support against 49.85 per cent for his rival, five-time loser Wavel Ramkalawan.
The opposition Seychelles National Party (SNP) claim neither won an outright majority, arguing that 1,062 invalid votes should also be counted in the overall total.
"We say that all votes in the box should be counted," Bernard George, SNP lawyer, told the Seychelles New Agency.
The appeal hearing in Victoria, the capital on the Indian Ocean archipelago's main island of Mahe, is expected to take up to three months.
A former British colony, the Seychelles is made up of 115 islands lying off the coast of east Africa, some scattered up to 1,000 kilometres from Victoria.