Moore, a Republican, is an anti-LGBT, religious right extremist who was twice removed as chief justice of the Alabama Supreme Court - the first time for refusing to take down a Ten Commandments monument from the state courthouse, the second time for trying to block marriage equality in the state.
Moore lost the Alabama special Senate election after numerous women came forward with allegations of sexual misconduct against him.
Swearing-in ceremonies for Jones are set for January 3 when the Senate reconvenes from its winter break.
And Alabama Secretary of State John Merrill told the Associated Press that despite Moore's lawsuit, Jones is still set to be certified the victor at that time.
Democrat Doug Jones was formally declared the victor of the bitterly contested US Senate race in the southern state of Alabama on Thursday, whittling down the Republican majority in the chamber by a crucial seat.
Democrat Doug Jones' historic victory over Republican Roy Moore was declared official Thursday as Alabama election officials certified him the victor of the special Senate election earlier this month, despite claims of voter irregularities from his opponent.
"I have stood for the truth about God and the Constitution for the people of Alabama", he said. His filing on Wednesday in the Montgomery Circuit Court sought to halt the meeting scheduled to ratify Jones' win on Thursday.
Moore did not concede the race to Jones and continues to raise funds with supporters in order to investigate claims of voter fraud.
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A spokesman for Jones earlier called Moore's lawsuit a "desperate attempt ... to subvert the will of the people".
Moore and Jones ran for the Senate seat vacated by Jeff Sessions, a Republican who became the USA attorney general.
Prominent conservatives who allege voter fraud is more prevalent than evidence now suggests declined to add their voice to Moore's complaint. "It's time to move on".
On election night, Moore had pegged his hopes on votes from military serviceman and provisional ballots.
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.
He denies the allegations and says they are politically motivated.
It cited "irregularities in 20 precincts" of the state's Jefferson County which it said were "enough to reverse the outcome of the election", quoting the views of conspiracy theorist Richard Charnin who claims the 2004 presidential election and 2016 Democratic primary were also rigged.
The number has been raised to 118 voter fraud complaints, with 85 so far having been adjudicated, Merrill said.