“There is this energy here, this feeling that anything can happen,” said Lesley Téllez, a Californian whose three-year-old business running culinary tours served hundreds of clients here last year. “It’s hard to find that in the U.S.”

The shift with Mexico’s northern neighbor is especially stark. Americans now make up more than three-quarters of Mexico’s roughly one million documented foreigners, up from around two-thirds in 2000, leading to a historic milestone: more Americans have been added to the population of Mexico over the past few years than Mexicans have been added to the population of the United States, according to government data in both nations.

Mexican migration to the United States has reached an equilibrium, with about as many Mexicans moving north from 2005 to 2010 as those returning south. The number of Americans legally living and working in Mexico grew to more than 70,000 in 2012 from 60,000 in 2009, a number that does not include many students and retirees, those on tourist visas or the roughly 350,000 American children who have arrived since 2005 with their Mexican parents.

“Mexico is changing; all the numbers point in that direction,” said Ernesto Rodríguez Chávez, the former director of migration policy at Mexico’s Interior Ministry. He added: “There’s been an opening to the world in every way — culturally, socially and economically.”