The company was still calculating the exact percentage of shares that voted, spokeswoman Kathy Shepard said.
Under terms of the buyout, Blackstone will pay Hilton shareholders $47.50 per share in cash. Including assumed debt, the total deal is valued at $26 billion (18.75 billion EUR).
Shares of Hilton Hotels rose 14 cents to $46.12 during afternoon trading. Blackstone Group shares rose 23 cents to $23.88.
The transaction must still pass regulatory approval.
Beverly Hills-based Hilton Hotels operates more than 2,800 hotels around the world. The company generated $8.11 billion (5.85 billion EUR) in revenue last year.