The local authority plans to close more than half of the centres by March 2017 unless groups take them over.
There were fears that an earlier pledge not to charge struggling centres rent would be limited to six months.
But a year has now been agreed, with one councillor saying six months would be "draconian" and "arbitrary".
The relief could potentially affect eight centres which are based in buildings where the council sets the rent saving them up to £38,493 each a year.
Local Green Party leader David Williams put forward the original motion and said the council's decision will provide campaigners with "an early Christmas present".
Cabinet member for property Lorraine Lindsay-Gale said the council had "listened very carefully" to the concerns raised and had extended the period "to help community-led services get off the ground".
She added: "We've already approved start-up funding for six proposals, a further eight are supported in principle and others are coming to fruition.
"Everyone wants this to be a success and the response of local communities continues to suggest it will be."
Giving rent relief for the eight buildings will lose the council about £155,000 a year but it would have to repay more than £1.5m to the government in 2017/18 if they are no longer used for children's services.
The county's 44 centres will be replaced with a network of 18 council-run centres when it withdraws funding for some non-statutory services to help save £6m.
One-off council grants, totalling £163,000, have been given to six communities to help them set up their own groups, while another eight have funding agreements in principle.
Oxfordshire County Council has agreed to waive the rents of children's centres run by community groups for up to a year if they face closure.