Bloomberg Associates will be run by George A. Fertitta, who as chief executive of the city’s tourism agency oversaw a record increase in annual visitors to New York, to 54 million this year. Mr. Fertitta said in an interview that the group would eventually expand to about 20 to 25 employees, most of them drawn from the mayor’s office, who will work closely with Mr. Bloomberg’s sprawling charitable foundation, Bloomberg Philanthropies. (Like the foundation, the consultancy will be housed inside a giant townhouse on the Upper East Side, around the corner from the mayor’s home.)

The consulting group is the latest chapter in Mr. Bloomberg’s long journey from political neophyte to much-admired mentor to fellow mayors, dozens of whom have flocked to City Hall to study his open-seat bullpen layout, attended his conferences about urban innovation and applied for grants from his foundation (called “mayors’ school” by several city leaders who have spent time there).

Image Mayor Michael R. Bloomberg Credit... Justin Sullivan/Getty Images

Mr. Bloomberg’s influence has already reached from Miami to Los Angeles, Chicago to Newark.

Mayor Mitchell J. Landrieu of New Orleans recalled receiving a $4 million grant from Mr. Bloomberg last year to hire a team of eight outside experts that advised the city on how to lower its murder rate. Since then, the city has created a multiagency team to combat gang activity, set up a midnight basketball league to keep young men off the streets and pushed to make it harder for those charged with gun crimes to get out of jail.

The murder rate in New Orleans has fallen by 17 percent this year.

“To his credit,” Mr. Landrieu said of Mr. Bloomberg, “this guy is putting his personal money into making city government work better.”

Mr. Bloomberg, a careful student of numbers, argues that investments in cities make mathematical sense: More than half the world’s population lives in urban areas, a figure expected to surge to about 70 percent over the next 40 years. The larger the city, the likelier that a big idea will catch fire and be adopted elsewhere, as the mayor showed with his ban on smoking in restaurants and trans-fats in foods.

“Great cities steal ideas from each other,” said Edward Skyler, a former deputy mayor in Mr. Bloomberg’s City Hall and now a top executive at Citigroup.