CNN forced Ms Brazile to resign as an on-air contributor in October 2016 after emails revealed that she had tipped off Ms Clinton's aides about questions likely to be asked by CNN moderators during the debates and town hall meetings carried by CNN.
At the time, Ms Brazile was highly supportive of Ms Clinton's candidacy. The network said the leaking of the question was a break of its ethics and undermined the impartiality of its campaign coverage.
Fox said Ms Brazile would comment on the upcoming presidential campaign on Fox News and Fox Business Network.
In announcing Ms Brazile's hiring, it made no mention of the issues surrounding her in 2016.
The DNC, which Ms Brazile led on an interim basis during 2016, decided earlier this month to exclude Fox News from televising any of its candidate events.
The organisation's chair, Tom Perez, said Fox was too closely aligned with President Donald Trump, leading him to conclude the network could not host "a fair and neutral debate for our candidates."
In a statement released on Monday, Ms Brazile said: "I know I'm going to get criticised from my friends in the progressive movement for being on Fox News. My response is that, if we've learned anything from the 2016 election, it is that we can't have a country where we don't talk to those who disagree with our political views.
“There's an audience on Fox News that doesn't hear enough from Democrats. We have to engage that audience and show Americans of every stripe what we stand for rather than retreat into our 'safe spaces' where we simply agree with each other."
People at Fox said Ms Brazile would have no role in commenting on any debates or town hall meetings it covers, though Fox will probably have very few of those given the DNC's decision to remove it from consideration in televising Democratic events.
Ms Brazile's role in channelling questions to Ms Clinton came to light in emails released by WikiLeaks during the final weeks of the 2016 presidential campaign. The emails came from a hack of the DNC's servers by Russian operatives.
CNN said at the time that it was "completely uncomfortable with what we have learned about (Ms Brazile's) interactions with the Clinton campaign while she was a CNN contributor."
Ms Brazile apparently got her information from conversations with TV One host Roland Martin, who was a guest moderator for one of the CNN debates. She said she learned that one of the questions during a televised town hall meeting in March of that year would involve the death penalty.
Another question before a debate with Ms Clinton's chief Democratic primary challenger, senator Bernie Sanders, I-Vt, in Flint, Michigan, concerned the city's ongoing water crisis, although it seems questionable that such a tip was helpful, given that the issue was bound to come up considering the event's location.
Ms Brazile said at the time that she offered her resignation when the WikiLeaks emails surfaced showing her telling a senior Clinton adviser, "From time to time, I get the questions in advance."
Ms Brazile was scheduled to make her first appearance on Fox on Monday afternoon.
The Washington Post