The closure is part of a deal worked out with record companies who sued the service claiming it was harbouring pirated pop.
In a statement on its website, Grooveshark said it had failed to get licences for the copyrighted music shared on the service.
It has also agreed to delete the music it offered and hand the website and apps over to the record industry.
"We made very serious mistakes," said the statement. "We failed to secure licences from rights holders for the vast amount of music on the service.
"That was wrong. We apologise. Without reservation," it said.
The shut-down also ends the legal action started by Warner, Sony, and Universal Music in 2011.
Pre-trial hearings for that case were heard earlier this week during which the judge in the case described Grooveshark's copyright violations as "wilful".
It was accused of illegally sharing almost 5,000 songs which meant that, if it had been found guilty, it would have faced a damages bill of up to $736m (Â£480m). Although Grooveshark's defence against the charges would probably have reduced the overall damages it would have faced.
The threat of the large bill has been lifted with the ending of the legal action. However, the terms of the settlement with the music industry mean the service's founders could still face a financial penalty if they do not respect its terms.
"This is an important victory for artists and the entire music industry," said the Recording Industry Association of America in a statement.
It said Grooveshark had built its business without providing proper compensation to artists.
"This settlement ends a major source of infringing activity," it said.
Grooveshark was set up in 2006 and had, at its peak, about 35 million users per month who were allowed to upload any song they chose. Employees at Grooveshark also uploaded songs to expand the library of music available to users.
Music-streaming service Grooveshark has announced that it is shutting down.