The legislation would establish a licensing collective, to be overseen by songwriters and publishers, and paid for by the digital services, with rights information maintained by the copyright owners. Digital services, which now must track down rights holders or file notices in bulk with the Copyright Office, will be able to receive blanket licenses from the collective. In exchange, the services will gain protections against lawsuits.

In a lawsuit filed late last year, for example — just before a cutoff date set by the bill — a music publisher representing songs by Tom Petty, Stevie Nicks and others sued Spotify for $1.6 billion over licensing lapses. Under the Music Modernization Act, the licensing collective would serve as a one-stop shop to obtain those rights.

Some Republicans on the Judiciary Committee, including the Texas senators John Cornyn and Ted Cruz, expressed reservations on Thursday about a collective established by the government rather than the free market, but still voted in favor of the bill.

Christopher Harrison, the chief executive of the Digital Media Association, a group that includes Google, Apple and Amazon, said that the new process would remove the bad faith that has existed between music publishers and streaming services.

“I describe those conversations as like the end of a Tarantino movie, where everybody is pointing guns at each other and claiming it’s the other person’s fault,” Mr. Harrison said. “We had a number of really frank conversations with publishers, saying, ‘Let’s get past who is to blame and figure out how to solve the problem.’”

A critical element of the bill would allow musicians to be paid for digital plays of recordings made before 1972, which are not covered by federal copyright. At a Senate hearing last month, Smokey Robinson called that rule unfair. “An arbitrary date on the calendar,” he said, “should not be the arbiter of value.”

The bill also includes two provisions favored by Ascap and BMI, the industry’s two biggest royalty clearinghouses, over the complex procedures used to set royalty rates in federal courts.