He unexpectedly lost to Jones by about 20,000 votes in the special election to fill the Senate seat vacated by Jeff Sessions, who is now USA attorney general.
"This is not a Republican or Democrat issue as election integrity should matter to everyone", Moore said in a Wednesday statement accompanying the complaint.
Swearing-in ceremonies for Jones are set for January 3 when the Senate reconvenes from its winter break.
Jones pulled off a massive upset in mid-December, edging out former Judge Roy Moore.
Merrill said the allegations of voting irregularities by Moore's team had been thoroughly investigated and found to be baseless, while a judge threw out a suit seeking to delay the results certification.
Alabama Secretary of State John Merrill is pictured shortly after certification of the special election. The seat was previously held by Republican Jeff Sessions, who was tapped by U.S. President Donald Trump as attorney general. Moore, 651,972, 48.3 percent and write-ins, 22,852, or 1.7 percent.
Democrat Doug Jones's election as US senator from Alabama was certified today, despite a lawsuit from opponent Roy Moore challenging the results. Luther Strange during a primary earlier this year and was widely expected to win the special election until he was accused of sexual misconduct by multiple women, when Moore was in his 30's and the women were as young as 14 years old. His filing on Wednesday in the Montgomery Circuit Court sought to halt the meeting scheduled to ratify Jones' win on Thursday.
Defeated U.S. Senate candidate Roy Moore reacted to Alabama finalizing the election results by again saying experts agree the election was "fraudulent".
"I am looking forward to going to work for the people of Alabama in the new year", Senator-elect Doug Jones said in a statement, calling his victory "a new chapter for our state and the nation". "This desperate attempt by Roy Moore to subvert the will of the people will not succeed", he told the Post. "It's time to move on", Sam Coleman wrote in an email.
Trump congratulated Jones after the unofficial vote counts were tallied, but said in a tweet sent later that day that "the deck was stacked against" Moore.
John H. Merrill, the Alabama secretary of state, has dismissed complaints, from Democratic and Republican critics, of election fraud. Moore denied the accusations and said in the lawsuit that he had passed a polygraph test to prove they are false. He said so far his office has found no evidence of fraud. In May this year, he ordered that a commission be formed to investigate voter fraud.
At this point, questions about Moore's guilt or innocence regarding the allegations against him are moot.
Porter and Bash went back and forth, with the CNN anchor shooting down claims of voter fraud.
"It's a very weak complaint, it does not rely on any election experts I've ever heard of and it makes claims that on their face do not appear to be plausible, or appear to be irrelevant", said Rick Hasen, an election law professor at the University of California, Irvine.