More than 2,900 athletes from 87 nations paraded before 40,000 people in the Fisht Stadium before President Vladimir Putin declared the Games open.
The Olympic flame was lit by Russian former triple gold medalists Vladislav Tretiak and Irina Rodnina as fireworks illuminated the night sky.
At a cost of $50 billion, the Sochi Games is the most expensive Olympics in history.
International Olympic Committee president Thomas Bach used his welcome speech at the ceremony to promote Olympic values of diversity and non-discrimination.
“The Olympics are about building bridges to bring people together,” Thomas Bach said.
“They are not about erecting walls to keep people apart. Embrace human diversity and unity.”
President Barack Obama and UK’s PM David Cameron stayed away from the ceremony, which was attended by 44 heads of state.
Vladimir Putin avoided making a political statement as he stuck to protocol by using a single sentence to declare the Games open.
Spectators inside the stadium and television viewers worldwide were treated to a glittering show lasting nearly three hours and featuring 22 tonnes of fireworks.
In a grand finale, tennis star Maria Sharapova, who grew up in Sochi, carried the Olympic flame into the stadium before it passed through the hands of pole vault world record holder Yelena Isinbayeva, wrestler Aleksandr Karelin and gymnast Alina Kabaeva,
It was carried out of the arena by former figure skater Irina Rodnina and ice hockey player Vladislav Tretiak, who lit the cauldron in the middle of the Olympic park while Igor Stravinksy’s Firebird Suite filled the stadium.
In a break from Olympic tradition, the teams had earlier entered in the order of the Russian alphabet, with the host nation coming in last to deafening cheers.
Athletes from the competing nations appeared to emerge from their country’s map courtesy of a dazzling light show.
While some nations – including Nepal, Mexico and Pakistan – are sending only one competitor, the US team of 230 athletes is the largest in the history of the Winter Games.
The US have never appeared at an Olympics on Russian soil having boycotted the Moscow summer Games in 1980.
The ceremony featured a colorful journey through Russian history, celebrating the country’s rich heritage in art, music and ballet, with 3,000 performers and 2,000 volunteers taking part.
In a moving sequence the lights were lowered as performers, dressed in white to symbolize peace, danced to the strains of Pyotr Ilyich Tchaikovsky.
Hosting an Olympics for the first time since 1980, Russian athletes are under pressure to improve on the embarrassment of 11th place at the last Winter Games in Vancouver.
Russia has devoted $940 million to elite winter sport since winning the bid to host these Games seven years ago.
The first medals of the Games will be decided on Saturday with five golds up for grabs in biathlon, cross country skiing, freestyle skiing, snowboarding and speed skating.
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