“Thanks to my family, friends and fans for their interest and well wishes,” he wrote.
Dre, whose real name is Andre Young, was taken to the hospital’s ICU on Monday where doctors ran tests to find what caused the bleeding on his brain.
He is in the middle of a divorce from wife, Nicole Young, who filed to end their marriage of more than 20 years.
Ms Young cited irreconcilable differences as the reason for the split.
Dre and Ms Young have two adult children together, 23-year-old son Truice and 19-year-old daughter Truly.
Fellow entertainer LL Cool J took to Twitter to send the former NWA star his best wishes.
“Dre is recovering nicely,” the rapper and actor tweeted.
Earlier Missy Elliott sent her prayers to the rapper on Twitter.
“Prayers up for Dr. Dre and his family for healing & Strength over his mind & body,” she tweeted.
The rapper, who was born in Compton, California, rose to fame in the rap group NWA in the 1980s.
After leaving the group he went on to huge solo success and won a Grammy for his 1993 album The Chronic.
The Compton-born rapper first came to prominence as a cofounder of the pioneering gangsta rap group N.W.A.
He went on to work as a hit music producer, and played an influential role in the careers of rappers such as Eminem and 50 Cent.