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According to the Associated Press, Biden has won the state with roughly 52 percent of the vote - becoming the second Democratic presidential candidate since 1948 to claim victory in the longtime Republican stronghold.
Former astronaut Mark Kelly has also won the Arizona Senate seat once held by John McCain.
Kelly defeated Republican Senator Matha McSally, who was appointed to the seat after McCain's death in 2018.
Before the race was called, Kelly said he was 'confident that when all the votes are counted, we're going to be successful in this mission'.
The news follows controversial comments from President Trump, as he claimed he had 'won the US presidential election' - despite the fact that the votes are still being counted.
Trump, 74, also said that if he wasn't named the winner, it would be one of the biggest frauds in the country's history.
Speaking at the White House, he said: "We were getting ready for a big celebration. We were winning everything.
"This is a fraud on the American public. This is an embarrassment to our country.
"We were getting ready to win this election. Frankly, we did win this election."
He went on to demand that 'all voting be stopped', despite the fact there is no evidence that votes were being made after the polls closed.
Trump also threatened to challenge the election results in the supreme court, adding: "We will be going to the US supreme court. We want all voting to stop."
Meanwhile, earlier in the evening, Biden told his supporters that he was confident of victory.
Speaking to a crowd of people in Delaware, the 77-year-old thanked his fans for their patience.
He said: "Good evening. Your patience is commendable. We feel good about where we are."
Biden added: "We knew this was going to go long, but who knew we would go into maybe tomorrow morning, maybe even longer!
"But we feel good about where we are. I'm here to tell you tonight we believe we're on track to win this election.
"It ain't over until every vote, every ballot is counted."
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