Vivek Ramaswamy, the 38-year-old entrepreneur and political newcomer who briefly made a splash with brash policy proposals and an outsize sense of confidence, dropped out of the race for the Republican White House nomination after a disappointing fourth-place finish in the Iowa caucuses.

He then immediately endorsed former President Donald J. Trump for the White House.

“We did not achieve the surprise that we wanted to deliver tonight,” he said in Des Moines on Monday night.

Mr. Ramaswamy, who funded much of his campaign from a personal fortune made in biotechnology and finance, was an unlikely contender at one point. He clung closely to Mr. Trump, vowing to support him even if he was convicted of felonies, promising to pardon him if elected to the White House, and saying he would voluntarily remove his name from the ballot in states that succeeded in knocking Mr. Trump from the ballot as an “insurrectionist” disqualified by the Constitution.

Then two days before the Iowa caucuses, Mr. Trump’s campaign turned on him, declaring him a fraud, and the former president — after months of warmth toward his would-be rival — demanded that voters reject Mr. Ramaswamy and vote for him.