"Tomorrow President-elect [Joe] Biden and Vice President-elect [Kamala] Harris will be sworn in," McConnell said on the Senate floor. "We'll have a safe and successful inaugural right here on the west front of the Capitol."
McConnell said Congress will move forward following the deadly riot at the Capitol building on January 6.
He also stressed that the Capitol riot was provoked by President Donald Trump and other powerful people using lies.
"The mob was fed lies. They were provoked by the President and other powerful people," McConnell said during remarks on the Senate floor.
Trump was impeached by the US House of Representatives last week for "inciting insurrection" after a group of his supporters stormed the Capitol to protest lawmakers verify elector slates from US battleground states that Trump claims robbed him of electoral victory.
Although Trump will leave office on Wednesday, the next step in the impeachment process is for the Senate to hold a trial. It will take 67 votes in the 100-seat chamber to convict the president.
McConnell did not mention when the impeachment trial was expected to begin. He noted that the House of Representatives has not delivered the article of impeachment to the Senate yet.
In addition, McConnell said the victory in the November 3 election did not hand Democrats a mandate for a "sweeping ideological change."
The Biden inauguration is set to take place on Wednesday at around noon local time (17:00 GMT). Some 25,000 National Guard troops have been mobilized as part of enhanced security measures.