A final tally announced by Secretary of State Brad Raffensperger showed that Mr Biden won the normally Republican stronghold by under 12,000 votes.
The state carried out a second recount of the 3 November vote following challenges from President Trump's team.
Mr Raffensperger, a Republican, warned that debunked claims about voting fraud were "hurting our state".
President Trump continues to refuse to accept defeat in the vote, alleging, without evidence, there has been widespread fraud.