The Fairfax County School Board approved a new plan Thursday that will require neighboring districts to help cover a $90 million renovation of the Thomas Jefferson High School for Science and Technology through fixed-tuition costs.

The new proposal replaces an earlier plan by the school board to have surrounding counties pay a share of the construction through lump sums or additional costs.

The vote came after a closed session in which the board discussed a recent opinion by the state attorney general, who wrote that under current contractual agreements, surrounding counties do not have to help pay for the renovation of the magnet school, which draws students from within and outside Fairfax. According to Virginia law, Attorney General Kenneth T. Cuccinelli II (R) wrote, Loudoun County does not have to contribute to the renovation costs of a building outside of its district that it does not lease or partly own.

After Fairfax proposed the lump-sum payments in January, many counties questioned whether being eligible to send students to TJ, as the elite public magnet school is known, was worth the investment. About 20 percent of the school’s 1,815 students live outside Fairfax County.

Loudoun, which sends about 200 students to TJ overall, would have paid about $7.8 million in a lump sum or over a 30-year period under the original proposal. Cuccinelli wrote that such a plan might be illegal unless the fees were covered by fixed tuition.

On Thursday, the Fairfax board voted to amend the cooperative agreements in response to Cuccinelli’s decision. Under the new contracts, each school district would be required to pay a fixed tuition per student that would include fees to fund the new construction. The renovation, now underway, includes plans for high-tech science labs and solar panels that will help power the building.

According to the old agreements, Loudoun, Arlington and Prince William counties and Fairfax and Falls Church cities pay about $13,000 per student in tuition, which covers only operational costs.

School officials estimated that the new fixed-tuition costs may average at least $1,000 higher per student.

The fixed-tuition payments will ensure that Fairfax taxpayers aren’t the only ones footing the bill for the building that is used by about 350 students who live outside the county, said school board member Dan Storck (Mount Vernon).

“There’s no such thing as a free lunch,” he said. “We’ll be offering the surrounding school districts a reasonable and fair plan to pay for the renovation for a school that their students attend as well.”