The stadium is in Diamniadio, a town being built about 30 kilometres (20 miles) from the capital Dakar, for which an express train link opened in December.
The venue, to be named in honour of former president Abdoulaye Wade, will be the only one in Senegal certified for international football.
Current President Macky Sall said during an inauguration ceremony that the naming of the stadium was a “tribute to the multidimensional, intellectual, pan-Africanist politician”.
“This beautiful infrastructure — dedicated to young people — is an invitation to continue our path towards excellence,” Sall said.
The country’s last major stadium, Lat Dior, in the region of Thies 70 kilometres from Dakar, lost its certification from the Confederation of African Football (CAF) in May last year.
Jubilant crowds came by bus and train for the inauguration, which follows Senegal’s dramatic victory at the Africa Cup of Nations (AFCON) on February 6.
The new stadium was built in just 18 months by Turkey’s Summa construction company, at a cost of 156 billion CFA francs ($270 million, 238 million euros).
Sall, Turkish President Recep Tayyip Erdogan and FIFA boss Gianni Infantino were among the VIPs who attended the Tuesday’s inauguration.
An exhibition match was part of the show, with Senegalese legends such as Aliou Cisse — the current coach of the national side — opposing a team of African all-stars, including Cameroon’s Samuel Eto’o and Didier Drogba of Ivory Coast.
Mbaye Jacques Diop, a communications advisory at the ministry of sports, said the project was part of a programme to make Dakar a “sporting hub” for Africa.
It would mean an end to matches transferred to Asia because the continent lacked infrastructure, he said.
The first big competitive match will be on March 29.
Senegal, who beat Egypt to claim the African title will meet the Pharaohs again in a World Cup qualifier.
Senegal has launched a programme to refurbish its stadiums before Dakar hosts of the Summer Youth Olympics in 2026.
The country’s biggest sporting venue is the 60,000-capacity Leopold Sedar Senghor Stadium built in Dakar in 1985.