Capcom has confirmed that Street Fighter V on PlayStation 4 will be compatible with PlayStation 3 controllers.
Additionally, the final version of #StreetFighterV (on PS4) will be compatible with PS3 controllers.
— Street Fighter (@StreetFighter) February 9, 2016
Capcom verified this news after reports came out that an outlet with an advance copy of Street Fighter V downloaded a 5.9 GB patch that added this feature. Capcom promised they would look into adding this feature since May of last year. With this news, it is likely that the feature will be integrated into the final retail release.
Many fans, including the most hardcore Street Fighter fans, were hoping Capcom could add this feature in. In particular, many hardcore fans still prefer to play on arcade style joysticks, instead of the now standardized double analog controllers, like the Dualshock.
Fans wanted the feature so much that they looked for and used third party solutions to use their PlayStation 3 and USB arcade joysticks on the Street Fighter V beta. Many of them were able to make it work, even though they did it on an online beta. So, fans knew that Capcom was capable of making this happen, at least on a technical level.
In general, legacy support for game controllers and peripherals is determined by several complicated factors, including not just technology concerns, but also business considerations. You can learn more about this here. Street Fighter V fans are fortunate that Capcom was able to meet their request.