The city has paid $8.5 million to a Stuyvesant HS athlete who ended up a quadriplegic after a school-van accident, court records reveal.

Valerie Piro, now 22 and a junior at Harvard University, won the award in December, settling her 2008 Manhattan Supreme Court lawsuit. The city completed the payout this month.

The van was taking the Brooklyn girl, then 17, to a track competition in January 2008 when it careened off a Vermont highway and rolled over several times.

Piro, with no feeling from her chest down, took the SATs while rehabbing and got a near-perfect score.

The settlement figure is one of the city’s highest, said her lawyer, Fredric Eisenberg.

The Piro family wasn’t home yesterday and didn’t return calls for comment.

A spokeswoman for the city’s Law Department said, “We feel this settlement appropriately resolves the matter for all parties.”