George W Bush and his wife Laura have also announced plans to be there, saying they want to "witness the peaceful transfer of power".
The Manhattan business mogul will be sworn in as the 45th US president on Capitol Hill on 20 January.
Mr Trump defeated Mrs Clinton in November's election and castigated Mr Bush over the Iraq war and 9/11.
Before Tuesday's announcement, Jimmy Carter was the only former president to have said he would attend the nation's 58th inauguration.
