The move marks the first time Vaya will sell a sell a subsidised mobile handset with its plans.
The Galaxy S III 4G will be available for an additional cost of $34 per month as an add on to Vaya's Power Plan 22, 34 or 45 plans.
Combined with these plans, the total cost of the Galaxy S III 4G will be $56 per month, $68 per month, or $79 per month, respectively.
Last week, Vaya announced and released 4G mobile plans for the first time.
The plans start at $9 per month with a data allowance of just 100MB and range up to $45 per month with a 3GB data allowance.
Vaya's CEO, Ben Pullen, said the smaller plans with minimal data allowance are all about giving customers choice.
"There are still a substantial number of people who, regardless of 4G, still use their phone as a phone. For those people, we have a $9 plan whereby we keep the recurring cost as low as possible at the expense of included data."
"If someone does need extra data, for $7/month they can purchase an extra 1GB of data - customers can have as much as they like, for as long as they like, month by month. Customers can even add these mid-month to avoid any potential overspend."
All Vaya plans can be purchased on both month to month and 24 month contracts. New customers will receive 20 per cent off the monthly plan price for a maximum of 24 months on all plans.
The Samsung Galaxy S3 4G will be available through Vaya from Friday 18 April.