Photo: (AP Photo/Matt Rourke)
The recount was initiated by Green Party presidential nominee Jill Stein, who is also seeking recounts in Michigan and Pennsylvania, citing “statistical anomalies”.
Results would need to be overturned in all three states to alter the outcome of the election.
Donald Trump, who narrowly won Wisconsin, called the move a “scam”.
The president-elect said it was a way for Dr Stein – who is funding the recount through public donations – to “fill her coffers with money”.
“The results of this election should be respected instead of being challenged and abused,” he said.
‘Obligation’
The Clinton campaign’s general counsel, Marc Elias, said the Clinton team and outside experts had been “conducting an extensive review of election results, searching for any signs that the voting process had been tampered with”.
He said there was no evidence to conclude the election was sabotaged, but “we have an obligation to the more than 64 million Americans who cast ballots for Hillary Clinton to participate in ongoing proceedings to ensure that an accurate vote count will be reported”.
Mr Elias noted that the number of votes separating Mr Trump and Mrs Clinton in the closest of the three states - Michigan - ”well exceeds the largest margin ever overcome in a recount”.
However, he said the campaign would join in “on principle” in the Midwestern states if Dr Stein follows through on her promise.
The Green Party nominee reportedly wants to be sure computer hackers did not skew the poll in favour of Mr Trump.
Concerns over possible Russian interference had been expressed in the run-up to the vote.
The US government has said Russian state actors were behind hacks on the Democratic National Committee.
$7m fundraising target
In a statement on Friday, the Wisconsin Elections Commission said it had received two recount petitions from the Jill Stein campaign and from Rocky Roque De La Fuente, a businessman who ran unsuccessfully to be the 2016 Democratic presidential nominee.
Administrator Michael Haas said the count would begin in the week after Dr Stein’s campaign paid the fee, which the commission was still calculating.
Dr Stein’s campaign needs to raise millions of dollars to cover the fees for the vote recount in all three states.
Her website says over $5.8m (£4.65m) has already been raised toward a $7m target. It says this is enough to fund the recounts in Wisconsin and Pennsylvania.
