They will take office just as the Senate considers whether to convict President Donald Trump in an impeachment trial for inciting the deadly storming of the US Capitol and as President-elect Joe Biden seeks to jump-start his agenda after inauguration.

The two men are set to be sworn in to office on Wednesday afternoon shortly after Biden's inauguration, according to news releases issued by each.

The certification by Secretary of State Brad Raffensperger officially seals Warnock and Ossoff's victories over their Republican opponents in the January 5 runoffs.

Kelly Loeffler and David Perdue, both incumbents, conceded days after the election. Shortly after certification by Raffensperger, Governor Brian Kemp signed off on their certificates of election.

Official results from the secretary of state show Warnock beating Loeffler by about 93,000 votes out of nearly 4.5 million cast, or about 2 per cent, while Ossoff beat Perdue by about 55,000 votes, or 1.2 per cent.

Both margins are larger than the .5 per cent required to ask for a recount under Georgia law.

Once Warnock and Ossoff are sworn in, there will be a 50-50 partisan divide in the Senate, giving Vice President-elect Kamala Harris the tie-breaking vote.

Warnock will be the first African American senator from Georgia, while Ossoff will be the state's first Jewish senator and the Senate's youngest sitting member.

Their wins bookend a divisive and drawn-out election cycle that brought seismic shifts to Georgia politics and made the once reliably red state a key battleground.

Biden in November became the first Democratic presidential candidate to carry the state since 1992, while Warnock and Ossoff are the first Democrats to win a US Senate election in Georgia since 2000.

Australian Associated Press