In a statement on their website, the club said it hoped the initiative would "ease the financial burden on fans who follow City on their travels."
Stoke's chief executive Tony Scholes said in an interview on the site that he believed it was the first time any club in England's top four divisions had undertaken such a venture.
"As a club we are conscious that following football can be an expensive business, especially at a time when so many people are feeling the squeeze financially.
"We work hard to try and provide our supporters with value for money which is why we have not increased our ticket prices since being promoted to the Premier League in 2008.
"However, we realise how expensive following the club away from home can be for supporters and we're delighted to be able to offer free coach travel and hope it encourages more of them to give us their fantastic backing away from home."
The offer covers all 19 away league matches starting with the visit to Liverpool on August 17.
The new TV deal is worth around £5.5 billion for the Premier League over the next three seasons. As part of the deal each club gets a guaranteed increase of around 14 million pounds, not including increased prize money.
- Sports & Recreation
- Premier League