About 50,000 tickets will be sold over three days as part of a "phased approach" to manage demand on the website.
Glasgow 2014 said the breakdown of which events would be on sale for each day would be announced early next week.
An extra 100,000 tickets for the Games went on sale on Monday but problems started almost immediately, with complaints about long delays and issues with finalising transactions.
Sales were temporarily suspended in the early hours of Tuesday morning and after a second day of problems Glasgow 2014 suspended all sales until the issues could be fully resolved.
It also emerged some sports fans who called the dedicated phone line were charged while listening to an engaged tone, with some customers running up bills of more than £100.
Games organisers have been working with Ticketmaster, the website operator, to resolve the problems and Sport Minister Shona Robison met both parties on Thursday to check on progress.
The phone line that will be used from 10am on Wednesday will be a free number and all purchases will be posted free of charge, removing a previous £4.50 charge.
Glasgow 2014 chief executive David Grevemberg said: "While we sold more than 60,000 tickets through our ticketing website and hotline last week and saw the most incredible support and enthusiasm from the public, the experience of purchasing tickets was frustrating and unacceptable for some people.
"With additional measures in place aimed at managing demand and the addition of free postage on all orders and a freephone ticketing hotline, we aim to get back to the business of ensuring remaining tickets are sold and that thousands more people can begin to look forward to experiencing the excitement of the Games.
"While we cannot change the past experience of some of our customers, we do want to thank everyone for their huge support of the Games.
"Our focus now is on enabling everyone who wants to be part of one of the world's great sporting parties to be able to secure the tickets to do so."
The issues that forced sales to be suspended this week were branded a "shambolic fiasco" in the Scottish Parliament on Thursday.
Ticketmaster is also facing criticism for its role in the 2015 Rugby World Cup in England after postponing a ticket sale that was due to start yesterday.
Chris Edmonds, chairman of Ticketmaster UK, said: "We are pleased to confirm that we will be relaunching the Glasgow 2014 Commonwealth Games ticketing website next Wednesday, May 21.
"Our team has been working tirelessly to review, analyse and rectify the issues that were experienced on the site.
"Our priority remains to ensure that customers have the best possible experience when securing their tickets for the Games."
About 2.3 million applications were made for the initial one million tickets released last year, with athletics, aquatics and cycling the most popular events.
Ms Robison said: "Both Glasgow 2014 and Ticketmaster have listened to customer feedback and I believe the move to a phased rollout for this release of tickets is a sensible approach to alleviate pressure on the website and give people greater clarity on availability for individual events."