Thompson, 60, finished second in last week's nine-person primary election, winning 26 percent of the vote. De Blasio won 40 percent, in unofficial results released immediately after the election.
The city requires a runoff election if no candidate earns 40 percent of the vote. Thompson had hoped de Blasio's final vote might be below the threshold as votes were checked and absentee ballots were counted, but Thompson's withdrawal rendered the point moot, The New York Times reported.
Monday morning, Thompson stood with de Blasio and Gov. Andrew Cuomo, another Democrat, at City Hall and endorsed de Blasio, saying, "Bill de Blasio and I want to move our city forward in the same direction. This is bigger than either one of us."
The announcement clears the way for a general election contest between de Blasio, New York City's elected public advocate, and Republican Joseph Lhota, former Metropolitan Transportation Authority chairman. The winner will succeed Mayor Michael Bloomberg, an independent who previously had been a member of both the Democratic and Republic parties.