The rapper launched the service with major star backing, hoping to shake up the growing industry through high sound quality and artist control.
With veiled swipes at streaming leader Spotify, Jay Z brought out musicians including Madonna, Kanye West and the masked electronic duo Daft Punk, who will all be equity partners in the new Tidal.
Jay Z earlier this year bought Tidal (known as Wimp in some countries) which markets itself to audiophiles, by spending $56 million for its Swedish-listed parent company Aspiro.
At the announcement in New York, singer Alicia Keys hinted that some musicians could choose to release material exclusively or early on the artist-owned service.
"Tidal is dedicated to cultivating a sound business enterprise that promotes the health and sustainability of our art and our industry around the world," Keys said.
"We believe it is in everyone's interest — fans, artists and the industry as a whole — to preserve the value of music and to ensure a healthy and robust industry for years to come."
Tidal released a promotional video in which musicians accused unnamed streaming companies of treating them as mere commercial products.
"They are the carrier; we are the artists. Somehow things shifted and we went into the background, and it has to come forward," Madonna said.
Other artists who will be shareowners in Tidal — with the exact financial details not disclosed — include Jay Z's wife Beyonce, rocker Jack White, Coldplay's Chris Martin, rapper Nicki Minaj and R&B singer Rihanna.
Tidal said it was also working on the relaunch with Sprint, one of the major US cellular providers, which is owned by Japan's Softbank.
The artists signed a declaration to the sounds of Radiohead, the British experimental rockers who along with Taylor Swift have accused Spotify of devaluing music through meager payouts to artists.
Spotify has rejected the accusations, saying that it is a rare source of growth in music sales and has paid out $2 billion toward artists since 2007.
Streaming — which allows users to play unlimited on-demand music online — has quickly shaken up the industry, narrowly edging out CD sales in revenues last year in the United States.
Spotify, also from Sweden, says it has 60 million users with 15 million of them paying — usually $9.99 a month.
Unlike Spotify, Tidal does not offer a free service and is generally twice as expensive, at $19.99 a month, although for the relaunch, it also offered a more basic $9.99 service.
Tidal streams at 1,411 kilobytes per second — well above the 320 for premium subscribers of Spotify, which offers even lower levels for free users.
The difference means that Tidal offers higher sound quality for audiophiles with advanced sound systems — but that casual listeners using simple laptops or smartphones may face slower connections.
Tidal will also try to distinguish itself through ample videos.
Jay Z did not speak at the announcement, which came after hours of promotion for the relaunch on social media.
But he gave an interview to industry journal Billboard in which he billed Tidal as a new way for artists to experiment with form.
"It doesn't have to be three minutes and 30 seconds. What if it's a minute and 17, what if it's 11 — you know, just break format," Jay Z said.
He acknowledged that some music labels were nervous about the project but described it more as a "record store" than a new record company.
Spotify already has a range of rivals including US-based Rhapsody and Google Play.
Paris-based Deezer, which is strong in Europe, last year entered the United
States as a high-end-only service which, like Tidal, uses FLAC rather than
more common MP3 files.
Apple — which pioneered digital music through iTunes in 2001 — has sought to expand in streaming as the market shifts away from permanent downloads.
Apple bought rap mogul Dr. Dre's Beats and is reportedly planning an entirely new streaming service.
Tidal entered the United States late last year and operates in 31 countries, with six more to come this year including Australia and Germany.
Before Jay Z's purchase, Aspiro said it had 512,000 paying users for Tidal and sister service Wimp.