Chester Bennington's death certificate confirms the details we knew ... that the 41-year-old singer committed suicide with a belt.

According to the doc, obtained by TMZ, the Linkin Park singer died at 9:08 AM in his residence on July 20. The immediate cause of death is listed as hanging.

Chester's referred to as a "rock star musician" on the certificate, and had been in the music biz since he was 14 years old.

We broke the story ... Bennington died in his home nearly 2 weeks ago.