Wages would begin to rise next year, ultimately reaching $15 from Washington state's minimum of $9.32 over three to seven years, depending on the business.
One councillor said the vote "sends a message heard around the world".
US minimum wage is $7.25, although 38 states have set higher levels.
The states of California, Connecticut and Maryland have recently passed laws increasing their respective wages to $10 or more in coming years.
Nationally, US President Barack Obama has called for a $10.10 federally-mandated minimum wage, which would require action by the divided US Congress.
Under the plan, firms with more than 500 employees nationally will be given at least three years to phase in the increase, those who provide health insurance subsidies would get four years and smaller businesses would be given seven years.
Click here to read more and to see a map of the U.S. with minimum pay spreads across different states.