The announcement, first made in a series of tweets by the South Carolina Republican and Trump supporter, came as Giuliani has become targeted in House Democrats' impeachment inquiry.
Graham went on to claim that the House's impeachment inquiry forced his hand in the matter, making the statement within an hour after House Intelligence Committee Chair Rep. Adam Schiff (D-CA) accused the Trump administration of "obstruction" for objecting to the testimony of key witnesses in the impeachment inquiry.
But Graham tweeted Tuesday, "Given the House of Representatives' behavior, it is time for the Senate to inquire about corruption and other improprieties involving Ukraine", and cited actions leading to the firing of Ukraine's top prosecutor.
With the US ambassador to the European Union Gordon Sondland sidelined in his desire to appear and answer questions, cable TV regular Giuliani will get the chance to air his claims of Ukrainian corruption that he wants aired. Giuliani has drawn massive scrutiny over his media tours in defense of the president, the latest of which, he used to proclaim Trump has "every right" to ask foreign powers to investigate Biden.
But it also would put Giuliani on the record about his months-long public and private effort to push Ukraine's government to launch a probe even as Trump himself was blocking military aid to Ukraine's new government.
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Senate Judiciary Committee Chairman Lindsay Graham said earlier that he would invite Giuliani to testify before his committee.
House Democrats are centering their impeachment inquiry on allegations that Mr. Trump and his officials attempted to pressure Ukraine into opening an investigation into the Biden family. Kamala Harris (D-Calif.), Cory Booker (D-N.J.) and Amy Klobuchar (D-Minn.) - an opportunity to question him.
Giuliani has stated that he shared all of the details of his conversations with Yermak with the State Department.
"Democratic members have plenty of questions for Mr. Giuliani and this would give us an opportunity to help separate fact from fiction for the American people", Senator Dianne Feinstein, the committee's top Democrat, said in a statement.
Trump and Giuliani also have suggested that Ukraine was involved in interfering in the 2016 election as they've sought to undermine the origins of Special Counsel Robert Mueller's probe into Russian election meddling, an allegation Ukrainian officials have rejected. Graham has moved to seize the opportunity and start investigating what the Judiciary Chairman has called "disturbing allegations" and "corruption" surrounding the firing of the Ukrainian prosecutor investigating Hunter Biden.