Sonia Gandhi's party and its allies took 214 of the 539 seats in the national parliament of the world's most populous democracy, while Vajpayee's Bharatiya Janata Party (BJP) and its allies attained 187 seats.
More than 370 million people voted in elections held on five days since April 20.
The BJP has led ruling coalitions since 1996, and was widely expected to win again, after Vajpayee called an early election, hoping to capitalize on healthy economic growth and the 79-year-old premier's popularity, which was boosted when he launched a personal peace drive with longstanding rival Pakistan.
Congress, meanwhile, campaigned on a platform of reaching out to India's huge rural poor population.
The Congress victory sees a return of the Nehru-Gandhi dynasty, with both Sonia Gandhi and her son, Rahul, winning their seats.
Despite some opposition by Hindu nationalists, the Italian-born Sonia Gandhi is expected to become prime minister, although Congress has yet to make an announcement to that effect.
Sonia is the widow of former prime minister Rajiv Gandhi, who was killed by a Tamil suicide bomber in 1991. Rajiv Gandhi's mother, Indira, served earlier as prime minister, but she too was assassinated, by her bodyguards in 1984.
Raised a Catholic, she has said she supports the idea of an India that will encompass all religions.
Eighty percent of the country's more than one billion people are Hindus, while its 140 million-strong Muslim minority is the second largest Muslim community in the world, after Indonesia.
During the BJP era, violence between Hindus and Muslims cost thousands of lives, especially during riots in the BJP-ruled Gujarat state two years ago.
BJP rule also saw some difficult times for India's Christian minority, comprising just 2.5 percent of the population.
The BJP is affiliated with some extremist Hindu organizations. One of them, the National Volunteer Corps (Rashtriya Swayamsevak Sangh or RSS) has long accused Christian missionaries of luring poor Hindus to Christianity with inducements including money, education and health care.
In recent years, Gujarat and other states have seen some 200 attacks on Christians and their institutions, most attributed to the RSS and other similar groups.
Several U.S. congressmen have at various times urged the Vajpayee government to curb violence against Christians.
All-India Christian Council (AICC) president Dr. Joseph D'Souza said in a recent conference that the elections were a "make or break" time for India, where Christians and other minorities had long been persecuted.
"T he nation has seen what the Bharatiya Janata Party dispensation ...has done for the last five years," the ACC said. "The party has systematically eroded most of the fundamental freedoms of the citizen."
Government officials have argued that incidents of violence against Christians were isolated and were not part of a general hate campaign against a particular community.
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