OMNY is being put in place by Cubic, a payments company behind the MetroCard and that oversaw London’s fare system. The project is expected to cost about $644 million — $200 million more than what the authority estimated in 2016.

The Metropolitan Transportation Authority, which oversees the subway and buses, is starting OMNY in phases, with the readers currently available on buses on Staten Island and at subway entrances on the 4, 5 and 6 lines between Grand Central Station in Manhattan and the Barclays Center in Brooklyn.

Subway officials are taking a slow, cautious approach after other cities have struggled with hiccups like defective readers and riders getting double charged. For now, riders can pay for one trip at a time at the full fare of $2.75. Monthly and weekly passes will not be available through OMNY until 2021.

The agency will offer a physical OMNY card in 2021, and the MetroCard will meet its demise in 2023. Subway officials say there will always be a cash option for New Yorkers who do not have bank cards or smartphones.

The idea has progressed in fits and starts. A decade ago, the authority’s chairman, Jay Walder, had wanted to bring “tap-and-go” cards to New York after he implemented the Oyster card in London. Officials wanted to phase out the MetroCard as early as 2012, but it did not happen, in part because credit card companies were slow to make their cards compatible.

The authority said in 2016 that it was soliciting bids from companies to install the system and would award a contract by the end of that year. That did not happen until October 2017.

The project cost rose by more than $200 million from an earlier estimate, transit officials said, because the scope grew to include things like incorporating the commuter railroads and funding for Cubic to run the “back end” technology that riders do not see.