There are some people both inside and outside the Met who speculate about whether Mr. Weiss had wanted the top job all along, something he has denied. Several art world executives, who asked to remain anonymous because they did not want to jeopardize their working relationships with the Met, have questioned Mr. Weiss’s decision to sound the alarm about a looming $40 million deficit, which contributed to a sense of a museum in crisis.

By bringing to light problems at the Met, as well as providing a positive alternative to Mr. Campbell’s leadership — improving communications with the staff and board, for example, — Mr. Weiss helped accelerate the board’s decision to urge the director out the door in February, making clear the status quo was untenable going forward.

Mr. Weiss, however, said he never gave the Met any ultimatum regarding the future management structure. “I said I want to be able to contribute meaningfully,” Mr. Weiss said in a telephone interview. “If they were going to bring in a new director to whom I would be reporting, that would have to make sense.”

Initial responses to inside the museum on Tuesday were positive. “Dan is the best person to see us through this transition,” said Keith Christiansen, the chairman of the Met’s European paintings department. “His art history background puts him in a very different category from previous presidents, he has a very good ear for curatorial concerns and we’ve already had good discussions with him. He’s a person I feel I can count on for listening and responding and taking action on curatorial concerns.”

Jeff L. Rosenheim, the Met’s chief of photography, added: “My colleagues and I support this appointment. We want to have the museum be strong and we want it to return to art and artists.”

While Mr. Weiss is well liked within the museum, he is not an obvious choice to lead the Met. A slight, bespectacled administrator with a Ph.D. in Western medieval and byzantine art and a master’s degree in art history, both from Johns Hopkins, Mr. Weiss comes out of academia and not art institutions.