Alabama Secretary of State John Merrill, a Republican, said he planned to ratify the results of the December 12 special election at 1:00 pm (1900 GMT).
"Will this affect anything?" Merrill said when asked on CNN about Moore's complaint of "systematic election fraud."
"The short answer to that is no."
Jones won 49.9 percent of the vote compared to Moore's 48.4 percent, a margin of nearly 21,000 votes out of 1.3 million cast in the southern US state, a Republican bastion.
A spokesman for Jones, the first Democrat to win a Senate seat in Alabama in 25 years, also said he did not expect Moore's challenge to go anywhere.
"This desperate attempt by Roy Moore to subvert the will of the people will not succeed," Sam Coleman told ABC News. "The election is over. It's time to move on."
The Alabama result dealt a stinging blow to President Donald Trump, who had thrown his support behind Moore, and narrowed his party's control of the US Senate to 51-49.
Trump easily defeated Democratic candidate Hillary Clinton in Alabama in last year's presidential election and Moore, a conservative Christian, appeared to be the favorite in the contest being held to fill the Senate seat held by Jeff Sessions, whom Trump had named attorney general.
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.
- Alleged 'irregularities' -
Trump congratulated Jones, a former federal prosecutor, on his victory but Moore refused to concede.
His campaign called late Wednesday for the certification of the results to be delayed pending a "thorough investigation of potential election fraud."
A lawsuit 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 campaign cited mathematician Richard Charnin, a president John F. Kennedy assassination conspiracy theorist who also asserts the 2004 presidential election and 2016 Democratic primary were rigged.
The complaint also contains an affidavit from Moore "stating that he successfully completed a polygraph test confirming the representations of misconduct made against him during the campaign are completely false."
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.
He was set to cruise to victory until allegations by several women -- first reported by The Washington Post -- that he assaulted, molested or pursued them when they were teenagers, including sexually touching one who was 14 years old at the time. Moore was at the time in his early thirties and working as an assistant district attorney.
Moore, 70, served twice as chief justice of the Alabama Supreme Court but was relieved on both occasions.
The second time was in 2016 for refusing to accept the US Supreme Court's ruling authorizing gay marriage.