All 171 attendees supported president Rob Flockhart's motion to fund its professional and performance set-up.
The decision hands the union an "immediate mandate" to seek inward investment.
"This was a pivotal moment for the game in Scotland," said Scottish Rugby chief executive Mark Dodson.
"I am delighted our members have empowered us to move forward.
"The hard work really does start now and we will now take time to prepare before entering a challenging market with what we think is a compelling and credible investment opportunity."
Scottish Rugby president Rob Flockhart added: "This vote will enable us to not only seek inward investment to the professional sides but also help to secure funding levels to our grassroots game and protect it from rising costs elsewhere in the game."
Any proposed investment would first have to be approved by the Scottish Rugby Board.
A two-thirds majority was required from the delegates when they gathered at Murrayfield on Friday.
In a statement last month, the union said there was "no immediate interest" from any external investor on the table.
Dominic McKay, the SRU's chief operating officer, said: "It's almost unprecedented in Scottish rugby to have an unanimous vote on something.
"I think everybody recognises that the challenge of running and operating two professional clubs is significant. The costs involved in running Glasgow Warriors and Edinburgh Rugby are rising.
"But we've got a responsibility as a governing body to make sure that we invest in all elements of our game and that includes the grassroots as well as the national team.
"So there's a recognition that if we want to be successful we can't do it on our own. The best way to do that is with external investment."