At a meeting Thursday night, the Santa Clara Valley Transportation Authority board of directors approved placing the measure on the upcoming ballot.
The additional income from the tax would fund the 16-mile extension from the Warm Springs BART station, an already approved extension from the Fremont station, in through Milpitas, San Jose and Santa Clara.
There will be six new stations under the plan, VTA spokeswoman Jennie Loft said.
"The regional importance of the BART extension to Santa Clara County cannot be overstated," VTA board Vice Chairwoman Dolly Sandoval said. The extension would create "an integrated rail service completely encircling the bay," she added.
VTA consulted with independent financial experts who provided a comprehensive analysis of the expansion's financial needs and decided that a one-eighth cent tax would be sufficient, according to the authority.
If the measure passes, the tax would not be assessed until the VTA secures state and federal funds to match local funds.