Speaking on the steps of the Lincoln Memorial in Washington DC, the president-elect also promised to bring change.
Among attendees at the two-hour event were his family, actor Jon Voight and Soul Man singer Sam Moore.
Mr Trump earlier laid a wreath at Arlington National Cemetery, Virginia.
Thursday evening's Make America Great Again! Welcome Celebration was open to the public and featured performances by country stars Toby Keith and Lee Greenwood.
"We're going to unify our country," Mr Trump said in brief remarks at the end of the concert.
