The last time it happened was in 1869, when outgoing president Andrew Johnson refused to travel to the ceremony in the same carriage as President-elect Ulysses Grant.
Trump announced his decision on Twitter.
Media outlets previously reported that Trump was planning to be at his golf course in Scotland, but Scottish First Minister Nicola Sturgeon said she would not allow him to enter the country.
It is now expected that Trump will leave the White House on 19 January and fly to his Florida base, Mar-a-Lago.
Trump yesterday conceded President-elect Joe Biden would take power, but still claims the election was stolen from him.
The inauguration is the formal ceremony that marks the start of a new presidency, and it takes place in Washington DC.
By law, inauguration day is 20 January.
In normal circumstances, Washington DC would see hundreds of thousands of inauguration revellers flock to the city, swarming the National Mall and selling out hotels - an estimated two million came when President Barack Obama was sworn in for his first term in 2009.
But this year, the celebration's size will be "extremely limited", Biden's team has said, and it has urged Americans to avoid travelling to the capital.
Biden and Vice President-elect Kamala Harris will still take their oaths in front of the US Capitol, overlooking the Mall (a tradition that started with President Ronald Reagan in 1981) but viewing stands that had been constructed along the parade route are being taken down.
In the past, up to 200,000 tickets were up for grabs to attend the official ceremony, but this year, with infections still surging across the US, only around 1000 tickets will be available.