Alabama Secretary of State John Merrill certified the results of the December 12 special election and dismissed claims of voter fraud by the campaign of the defeated Republican candidate, Roy Moore.
With Jones' upset victory in a Republican bastion, the party of President Donald Trump now holds 51 seats in the Senate and the Democrats 49 -- the slimmest of majorities.
The Alabama result dealt a stinging blow to Trump, who had thrown his support behind Moore, a conservative Christian.
But Moore's campaign was rocked in the final days of the race by allegations that the former judge had engaged in sexual misconduct decades ago, including molesting a teenage girl.
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Moore -- a former chief justice of the Alabama Supreme Court -- has refused to concede and even launched a last- minute legal challenge of the results, but a judge dismissed his suit, which called for certification of the results to be delayed.
Late Wednesday, Moore's campaign called for the certification of the results to be postponed pending a "thorough investigation of potential election fraud."
The suit filed by Moore's campaign cited "irregularities" in 20 precincts in Jefferson County, which it said were "enough to reverse the outcome of the election."
To back up the claims, Moore's team cited mathematician Richard Charnin, a conspiracy theorist who also asserts the 2004 presidential election and 2016 Democratic presidential primary were rigged.
Montgomery County Circuit Judge Johnny Hardwick however dismissed the complaint.
Moore, who has suggested the 9/11 attacks may have happened because of a lack of faith in God and argued Muslims should be barred from holding office, had wanted to bring his fiery brand of Christian religious activism to Washington.