The agreement—first reported by Dow Jones—would follow the rejection of a proposed $19 million deal with MasterCard, which needed approval from 90 percent of banks representing affected cardholder accounts.
"Target is pleased that we have reached a settlement agreement with Visa related to the data breach we experienced during the fourth quarter of 2013," the company said in a statement.
The settlement brings another step of closure to the retail giant after one of the largest data breaches in recent years, which exposed about 40 million credit and debit cards. The settlement costs were already reflected in Target's 2013 and 2014 results.
The deal with Visa will not require approval from a certain percentage of card issuers. In a statement Tuesday, a lawyer for the card issuers claimed the the deal did not go far enough to recoup losses.
"Importantly, it fails to fully reimburse card issuers for the substantial losses suffered from the Target data breach," said Charles Zimmerman of Zimmerman Reed, co-lead counsel for the plaintiffs.
The National Association of Federal Credit Unions also contended the settlement did not do enough to address the underlying issues.
"This settlement may be a start but much more needs to be done to make credit unions whole," said Carrie Hunt, senior vice president of government affairs and general counsel at NAFCU, in a statement. "Credit unions deserve to be fully compensated for their losses."
Target is scheduled to release its second-quarter results and hold a conference call Wednesday.
—CNBC's Courtney Reagan contributed to this report