"As I said on election night, our victory marks a new chapter for our state and our nation".
There were 1,348,720 votes cast in the election on December 12.
Moore lost the race to Jones by a margin of 1.5 percent - just under 21,000 votes.
The Democrat is not expected to take the Oath of Office and be officially seated in the Senate until early next year. Jones said he will be an "independent voice" in the Senate and will strive for "common ground with my colleagues on both sides of the aisle".
Prominent conservatives who allege voter fraud is more prevalent than evidence now suggests declined to add their voice to Moore's complaint.
Mr Jones will be sworn in on January 3 and is the first Alabama Democrat elected to the Senate in 25 years.
Mr Moore has been accused of multiple sexual abuses involving children.
Moore had refused to concede his loss to Jones and filed a last-ditch lawsuit hours before the certification, saying he believed there were voting irregularities that should be investigated.
Alabama officials certified the results of its special Senate election Thursday, officially naming Democrat Doug Jones the victor not long after a judge rejected a last-minute challenge from Republican Roy Moore.
Alabama Secretary of State John Merrill certified the election results at a meeting of the state canvassing board, which also includes Governor Kay Ivey and Attorney General Steve Marshall.
A spokesman for Mr Jones earlier called Mr Moore's legal action a "desperate attempt.to subvert the will of the people".
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"The election is over".
In a brief statement, Moore stood by his claims that the election was fraudulent and said he had to fight Democrats and over $50 million in opposition spending from the Washington establishment.
The lawsuit was filed the day before officials were due to certify Mr Jones the victor - two weeks after the vote.
Jones, a former USA attorney, claimed victory over Moore earlier this month, after various allegations of sexual misconduct plagued the Republican hopeful's campaign.
He said that the results could be re-tested if his accusers also submit to polygraph tests. He attached a statement from a poll worker that she had noticed licenses from Georgia and North Carolina as people signed in to vote.
His complaint alleges that out-of-state residents had been allowed to vote and that election fraud experts had concluded through statistical analyses that fraud had taken place.
The number has been raised to 118 voter fraud complaints, with 85 so far having been adjudicated, Merrill said.
Rick Hasen, an election law expert and professor at the University of California, Irvine, said Moore's complaint did not raise the sort of issues that lead courts to overturn an election.
Mr Merrill told the Associated Press on Wednesday that he had no intention of delaying the canvassing board meeting and certification of the victor.
Moore has sent several fundraising emails to supporters asking for donations to investigate claims of voter fraud.
He will takeover the seat previously held by Attorney General Jeff Sessions.