The rapper left UCLA Medical Centre in Los Angeles with Kim Kardashian and his doctor, Michael Farzam, multiple reports say.
Kanye West, 39, was admitted to hospital on November 21 suffering from “temporary psychosis due to sleep deprivation and dehydration”, said TMZ.
People magazine also quoted a source saying Kanye West was “home, getting some rest”.
Meanwhile, both CNN and the Los Angeles Times reported that he had left the UCLA Medical Center.
The LAPD responded to a report of a disturbance last week but later said it was a “medical emergency”.
Kanye West was admitted to hospital a day after he canceled his Saint Pablo tour after a series of rants on-stage.
The rapper ended a concert after four songs in Sacramento, California, before canceling a performance in LA a day later hours before he was due on stage.
Kanye West spent 10 minutes talking to the crowd about Beyonce, Jay Z, Hillary Clinton and Mark Zuckerberg during another show.
Kendall Jenner, Kim Kardashian’s half-sister, said the family had been praying for Kanye West as she spoke to reporters at the Victoria’s Secret fashion show in Paris.
Talking about Kanye West’s condition, Kendall Jenner told Entertainment Tonight: “Yes, of course [he’ll be OK].
“Everyone’s OK. Everyone is doing OK, [we’re] just praying.”
Meanwhile a E! Network representative said in a statement that the Keeping Up with the Kardashians reality show is “currently in production and has not been halted”.
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