Apple Music is getting bigger.

The music-streaming service told The Post on Wednesday it has reached the 40 million paid subscriber milestone. That’s up from the 38 million that Apple exec Eddy Cue disclosed at the South by Southwest tech conference last month.

By comparison, industry leader Spotify — which publicly listed its shares last week, fetching a market capitalization of $29 billion — disclosed in February that it had 71 million paying subscribers.

Separately, the Cupertino, Calif.-based tech giant said it has promoted Oliver Schusser to lead Apple Music’s global efforts, giving him the title of vice president of Apple Music & International Content.

Also on Wednesday, Sweden-based Spotify doubled down on its partnership with Hulu, saying all of its users will now get access to its ad-free music streaming service, as well as to Hulu’s limited-ad subscription TV service.

The bundle, which got rolled out to college students last fall, is called “Spotify Premium, Now with Hulu” and will give subscribers access to both services for $12.99 a month.

A normal Hulu membership would run subscribers $7.99 a month, while Spotify Premium costs $9.99 a month.

The offer is available now for current Spotify Premium subscribers and is expected to be available to everyone this summer, Spotify said.

Shares of Spotify dipped by as much as 2.1 percent Wednesday afternoon and were valued at $151.66 at 1:15 p.m.