U.S. District Judge Paul Magnuson gave his approval at a hearing Thursday in St. Paul, Minn.
"Target really needs to be commended for being willing to step up," Magnuson said.
The move will allow people to begin filing claims ahead of another hearing for final approval.
People covered by the settlement can file for up to $10,000 with proof of their losses, including lost time dealing with the problem.
A spokeswoman for Target says the class action didn't include people living in Canada.
Company documents say the Minneapolis-based company also faces one Canadian class-action stemming from the breach, which occurred at U.S. stores during the busy U.S. Thanksgiving shopping period.
Target's data breach in 2013 exposed details of as many as 40 million credit and debit card accounts and hurt its holiday sales that year. The company offered free credit monitoring for affected customers and overhauled its security systems.
The settlement would also require Minneapolis-based Target Corp. to appoint a chief information security officer, keep a written information security program and offer security training to its workers. It would be required to maintain a process to monitor for data security events and respond to such events deemed to present a threat.
"We are pleased to see the process moving forward and look forward to its resolution," Target spokeswoman Molly Snyder said in an emailed statement.
The company said in court documents filed in Minnesota that the funds for reimbursements will be kept in an interest bearing escrow account. Claims will mostly be submitted and processed online through a dedicated website.
Vincent Esades, an attorney for Target customers, said after the hearing that the settlement could end up costing Target $25 million, when attorneys fees and administrative costs are added in.
He said consumers will likely be able to start filing claims around April 30, and 100 million people may be eligible. Consumers can claim up to $10,000 if they can document losses; after those claims are paid out, the rest of the settlement funds will be divided among consumers who claim they suffered a loss, but don't have documentation.
Esades said customers who opt out of the settlement have the right to appeal.
Target attorney David McDowell declined to comment after the hearing.
The chain has worked hard to lure back customers that were hesitant to shop there after the incident. Over the 2014 holiday season, Target offered free shipping on all items. It recently announced that it was cutting its minimum online purchase to qualify for free shipping in half to $25. And on Wednesday the retailer said it will now allow returns for up to a year for its private and exclusive brands.
Target's bounce back from a turbulent stretch including the data breach and exit from Canada has been met with optimism on Wall Street. The retailer's stock traded above $80 for the first time Monday, reaching another in a string of all-time highs that it began to log just before the crucial holiday shopping season began in December.
Earlier this month, Target said it would lay off about 1,700 people, eliminate another 1,400 unfilled positions and cut up to $2 billion in costs. It will also focus more on technology to boost online sales growth. The latter move will involve about $1 billion aimed at beefing up business from shoppers who are more likely to shop online.
Target shares fell 62 cents to $80.44 in midday trading Thursday. It shares are up 35 per cent over the past year.
Associated Press writer Karnowski contributed from St. Paul, Business Writer Chapman from New York and The Canadian Press from Toronto.Suggest a correction