In addition to the dancers, the ceremony featured a large orchestra and opera singers, while drones formed pictures of ancient Egyptian gods above.
The pyramids, in the background, were illuminated with colourful lights, and fireworks were launched over the museum.
"I welcome you to your second home, Egypt, the land of civilisation and history, peace and love," President Abdel-Fattah al-Sissi said during the opening ceremony.
"I invite you to make this museum a platform for dialogue, a destination for knowledge and a meeting place for humanity," he added.
Drones also carried banners reading "Welcome to the land of peace" flying in front of the pyramids.
Saturday's inauguration comes nearly a decade after it was originally planned, due to economic crises, political upheavals, regional conflicts and the COVID-19 pandemic.
Deemed the world's largest museum dedicated to the ancient Egyptian civilisation, GEM showcases more than 100,000 ancient pieces spanning from the prehistoric era about 5000 BC to the Roman period about AD 400.
Eighty official delegations attended the opening, including 39 world leaders, the authorities said.
Denmark's Queen Mary, German President Frank-Walter Steinmeier, Greek Prime Minister Kyriakos Mitsotakis, Palestinian President Mahmoud Abbas and Jordan's Queen Rania were among the attendees.
The government declared Saturday a public holiday, and the evening ceremony was expected to be broadcast on large public screens across the country.
GEM has permanent exhibition halls, a children's museum, conference halls and an educational centre spread over 24,000 square metres.
The 5000-piece complete collection of King Tutankhamun, discovered in 1922, will be displayed for the first time together in one place, including the boy king's iconic golden mask.
The museum also houses the massive 3000-year-old statue of Ramses II, one of the country's most powerful ancient rulers.
The 11.3-metre-long statue, which weighs more than 80 metric tons, was relocated to the grand hall in 2018 while the museum was still under construction.
Another highlight is the 42-metre-long solar boat of King Khufu, or Cheops, unearthed in 1954.
First revealed in the early 1990s, GEM's foundation stone was laid in 2002 near the pyramids and the sphinx; construction began in 2005.
The $US1-billion ($A1.5-billion) project aimed to offer visitors more space as the museum situated in central Cairo's Tahrir Square was overcrowded with artefacts that were not properly displayed.
After its completion, the official inauguration was postponed several times.
Most recently it was moved from July to November after Israel waged a 12-day war against Iran.
Many halls have been accessible to the public for almost two years but the entire museum has been closed since mid-October for preparations ahead of Saturday's ceremony.
GEM is scheduled to reopen on November 4.
"Despite many obstacles, Egypt has finished a project that has been the dream of many people. We have finalised the largest museum in the world dedicated to one civilisation," Minister of Tourism and Antiquities Sherif Fathy said ahead of the opening.
He expects five million people to visit the museum yearly.
Right now, about 5000 people visit the museum per day, he said, expecting the number to reach 15,000.
Egypt hopes the official inauguration will boost its tourism industry - a main source of national income - as the Suez Canal revenues have been affected in the past two years by regional turmoil, since attacks by Yemen's Houthi rebels prompted many vessels to avoid the waterway.
In the first six months of 2025, Egypt registered 8.7 million visitors, a 22 per cent increase over the same period in 2024.
The tourism minister said 18 million visitors are expected by the end of the year.
