It will be the fourth operation in a year on the wrist for Ray. Initial reports listed a recovery of three months, but Joseph said that was not definitive.
"He's having surgery on Thursday in Houston," said Joseph. "Once that's done, we'll figure out what the timeframe is. He'll be back early part of the season."
Ray recently posted on his Instagram account that he was dealing with complications from a previous surgery and did not re-injure his wrist.
The injury limited Ray to eight games in 2017. He dislocated the wrist in preseason and started the year on injured reserve.
The 25-year-old Ray was activated at the end of October but went back on IR in December. He had only one sack after collecting 12 over his first two seasons.
"Both years, it never healed," said Joseph. "At first, he was a little down, but now he's back. He understands that he'll be back to help us and we can finally get it totally fixed so that he can play at a high level again. That's probably the exciting news to hear -- we know what it is and we can finally fix it the right way."
Denver opted not to pick up the fifth-year contract option of Ray early last month. Had the Broncos picked up his option, Ray would have received a salary of $9.232 million guaranteed against injury only in 2019.
In April's NFL Draft, Denver selected pass-rushing specialist Bradley Chubb, who is expected to start opposite All-Pro linebacker Von Miller.
A first-round draft choice of the Broncos out of Missouri in 2015, Ray collected four sacks as a rookie and eight in 2016, including three in a game against the Cincinnati Bengals.