Thompson has previously said he would hold out until every vote was counted. De Blasio was mere decimal points above the cutoff to avoid a runoff election, with 40.33 percent of the vote.
Thompson decided to concede after seeing that results would not change after a recount of voting machine tallies over the weekend.
He will reportedly concede at a "unity" press conference with de Blasio and Gov. Andrew Cuomo on Monday.
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