The Russian president was one of the last remaining leaders of major world countries to have held back on congratulating Biden.
"It's time to turn the page." "I'm convinced we can work together for the good of the nation," he said.
China was previously among a handful of major countries including Russia and Mexico that had not congratulated the president-elect.
Bush, as president and Biden then as chairman of the Senate Foreign Relations Committee had worked together on a number of issues during the Bush administration.
The villagers had earlier held special prayers for Harris' win and once they were answered, celebrated it with much fanfare on Sunday.
Netanyahu said he and Biden had "a long and warm personal relationship for nearly 40 years, and I know you as a great friend of Israel."
Biden defeated incumbent Republican US President Donald Trump in the closely-fought presidential election, according to the American media.
Biden, 77, and Harris, 56, would be sworn in as the president and vice president of the United States on January 20, 2021.
Harris vowed to fight to "root out systematic racism" but, like Biden, made a broad appeal to unity, saying that Americans "have elected a president who represents the best in us."
Promising "not to divide but unify," Biden reached out directly to Trump supporters, declaring "they're not our enemies, they're Americans."
The November 3 election saw a record voter turnout of 66.9 per cent, which is the highest turnout rate since 1900. The 1900 election had recorded 73.7 per cent voter turnout.
"We did win this election," Trump said in an extraordinary speech from the ceremonial East Room of the White House.
When last reports came in Biden had received 237 electoral college votes as against 213 of incumbent President Donald Trump of the Republican Party.
With a record more than 100 million Americans having voted ahead of Election Day due to the Covid-19 pandemic, definitive final results could easily take hours or even days to be tabulated.
With a huge expansion in mail-in voting to safeguard against the Covid-19 pandemic, nearly 100 million people have already cast ballots.
In Q2, many brands slowed or paused spending in reaction to US civil unrest, only to increase spend relatively quickly thereafter in an effort to catch up.
Some states key to the 2020 outcome were also firmly on the path to breaking records, such as Texas, where the Election Project said Sunday that 80 percent of the early 2016 vote had already turned out.
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