Boston’s public bike system is now owned by a company you call for a car ride.

The ride-hail firm Lyft announced a deal Monday to buy Motivate Co., the New York-based parent company that operates the Blue Bikes system in Boston, Brookline, Cambridge, and Somerville. Formerly known as Hubway, Blue Bikes allows riders to rent bikes at nearly 200 stations in the four communities.

The deal comes just months after Lyft’s rival, Uber, bought a similar bike-rental company, as ride-hail services seek to capture more of the overall transportation market.

For Lyft, it’s a chance to expand its footprint and business model in several major cities, including Boston, where tens of thousands of Uber and Lyft rides are taken every day. Motivate also operates public bike-rental systems in New York, Chicago, Washington, D.C., and other cities.

It also puts city governments into a direct working relationship with Lyft. Motivate operates the Blue Bikes system under a contract with Boston and the other communities. Local governments have no oversight over Lyft’s ride-hail operations, which are regulated by the state.

The deal comes at a time when traditional systems like Blue Bikes are being challenged by “dockless’’ upstarts whose bikes are not anchored to curbside stations. Instead riders use a smartphone app to locate and rent a bicycle, and drop it off wherever they like.

Dockless companies have begun rolling into cities near Boston, but are not allowed in the four Blue Bikes communities because of a promise of exclusivity with Motivate.

But Lyft said it will eventually bring dockless bikes to Motivate cities, as well as electric-powered vehicles. That would put the company on similar footing to Uber, which in April struck a deal to buy the dockless company Jump Bikes.

Tracey Ganiatsos, a spokeswoman for the Boston Transportation Department, said the city would welcome the new vehicle modes from Lyft.

“We are hopeful that the investment from Lyft will mean even more innovation in our system, including new bike technology and other improvements to our bikes and stations,’’ she said.

Terms of the deal were not disclosed. In a statement, Lyft said Motivate will remain a separate business unit, but the company plans to eventually allow users to rent bikes through the Lyft app — as they already can through a Blue Bikes app.

Adam Vaccaro can be reached at adam.vaccaro@globe.com. Follow him on Twitter @adamtvaccaro.