First there were little paper tickets that cost a nickel. Then there was the nickel itself, because until just after World War II, a nickel was the only thing that made subway turnstiles go around. Then came the dime, followed by the token — the singular currency of New York City. And, since the 1990s, there has been the MetroCard, recognizable, bendable, losable and not always reliable.

Now that familiar symbol of daily life is something else — outmoded. And it is on the way out.

On Monday, the city’s transit system took a significant step toward a more modern way for passengers to pay their fares. Starting late next year, they can do it the way Londoners already do, by waving cellphones or certain kinds of credit or debit cards at the turnstiles in the subway or the fareboxes on buses.

A committee of the Metropolitan Transportation Authority approved a $573 million contract for a new fare payment system adapted from the one in use for several years on the London Underground and London’s commuter railroads. New electronic readers will be installed in 500 subway turnstiles and on 600 buses in New York beginning late next year, and will reach the rest of the city’s subway stations and buses by late 2020.

“It’s the next step in bringing us into the 21st century, which we need to do,” said Joseph J. Lhota, the chairman of the transit authority. “It’s going to be transformative.”