The board voted 4-1 in favor of the change, with Supervisor Liz Kniss dissenting.
Kniss called the overlay method "a lousy idea."
"I don't think it's very sensible," Kniss said.
The change will not require any businesses or individuals in the county to change their existing number from the 408 area code.
Santa Clara County Chief Operating Officer Gary Graves said it is the method preferred by most affected parties over the other option, a geographic split.
Supervisor Ken Yeager said the overlay method is the better of two bad options.
"The problem is, neither choice is good and it's going to cause disruption whichever way we go," Yeager said.