At one point as Ms. Warren spoke, some scattered chants of “We trusted you!” and “Goldman Sachs” — a dig at Mrs. Clinton’s paid speechmaking — broke through the applause.

From the beginning of Mrs. Clinton’s monthslong search for a vice-presidential candidate, her consideration of Ms. Warren had seemed partly a matter of appearances, to appease liberals. Mrs. Clinton’s aides spread word of a meeting between the two Democrats, and Ms. Warren stopped by the campaign’s headquarters in Brooklyn, stoking speculation about her chances.

At first, Ms. Warren had wanted the No. 2 job, according to a person briefed on conversations with her operation, but she has since embraced her role as one of the Senate’s most outspoken liberal voices and a potential gadfly to a Clinton administration if Mrs. Clinton is elected and seeks to appoint officials from the financial sector to watch over the industry.

Democrats pointed to Ms. Warren’s successful effort last year to thwart President Obama’s appointment of Antonio Weiss, a senior investment banker at Lazard, to a top Treasury Department post, a victory that rallied the left when Mr. Weiss withdrew his name from consideration.

“Senator Warren will resume her role of being an advocate not just on the policy side, but certainly on the personnel side,” said Ilya Sheyman, the executive director of MoveOn.org Political Action.