In the lawsuit filed at the United States District Court for the District of Columbia, the election technology supplier said this "viral disinformation campaign" had damaged its reputation and laid the groundwork for the riots at the US Capitol.
It cited more than 50 statements by Giuliani on his podcast, at hearings and in the media, in which Dominion said he pushed the "demonstrably false" allegations in part for financial gain.
Claims that the presidential election was rigged, propagated by Trump and believed wholeheartedly by his supporters, have been rejected by courts in several states.
Giuliani falsely claimed Dominion's machines switched thousands of votes from Trump to Joe Biden. He claimed 6000 votes were switched in Antrim County, Michigan, even though state officials denied it and a hand count confirmed the voting machine figures.
New York State Bar Association (NYSBA) earlier this month launched an inquiry into removing Trump's lawyer from its ranks.
NYSBA said in a statement while they believe the violent uprising at the Capitol on January 6 was the fault of Trump, the President "did not act alone" and was aided by Giuliani, who called for "trial by combat" at a rally.
The legal association said it had received "hundreds" of complaints about Mr Giuliani and his attempts to overturn the election in recent months.
A group of prominent lawyers have also asked New York's judiciary to suspend Giuliani's law licence. Lawyers Defending American Democracy called for an investigation of the Trump lawyer, saying the complaint was "about law, not politics", in a letter signed by more than 50 lawyers.
The Cybersecurity and Infrastructure Security Agency said in a statement released after the 2020 vote that there was no evidence that voting machines were compromised and that the election was "the most secure in American history."
Dominion also filed a US$1.3 billion defamation lawsuit last month against lawyer Sidney Powell last month, who repeated the accusations in lawsuits. It has sent retraction letters to more than 150 individuals and businesses, including media outlets Fox News and Newsmax.
Giuliani told The Washington Post in a text message that the case would give him an opportunity to prove his allegations.
