Officers responded to a call at 2: 10a.m. on Monday and found him unresponsive. He was pronounced dead less than an hour later.
"At this point it is not a suspicious death and the manner will be determined by the medical examiner," a representative from the Austin Police Department in Texas told TVGuide.com on Tuesday.
Nance competed for Emily Maynard's affections back in Season 8, but was eliminated midway through the season. The former Bachelorette sent her condolences via Twitter.
"So sad waking up to the news about Michael Nance. Such a kind heart with so much talent. Sending prayers and love to his family and friends," Maynard wrote.
Several other Bachelorette contestants also reached out on social media.
A cause of death has not yet been determined.