MasterCard Inc. said its issuers have agreed to the terms of a settlement agreement it reached with Heartland Payment Systems over the processor's 2008 data breach.

The companies needed 80% of eligible MasterCard issuers to agree to accept an alternative recovery offer as part of the approval process for the $41.4 million settlement.

MasterCard said Thursday that 99% of the issuers eligible to be compensated under the settlement have agreed to it.

Under the deal's terms, MasterCard issuers can apply for reimbursement of fraud losses and operational costs related to accounts processed by Heartland in 2008 and thus exposed during the breach.

"This is an important outcome for our partnering financial institutions, and we are very pleased to announce that there has been overwhelming acceptance of the alternative recovery offers by our eligible issuing customers," Wendy Murdock, MasterCard's chief franchise officer, said in a press release.

The 2008 breach was one of the largest ever and has prompted many payments companies to consider stronger security measures, especially wider use of encryption.