PS4 crossplay will arrive when the Odyssey: Underworld update hits the console. Unfortunately, not everything will be supported when it arrives. Currently, cross-progression and cross-commerce are being worked on. So, players will have to wait a bit to have their achievements and trophies show up properly, or to use items purchased on other platforms.
For those curious about how the system will work, Titan Forge has provided a short FAQ, which can be found on the Smite site.
Additional good news… At least for those of you that play Paladins or Realm Royale. This is more or less a “we should have expected that” kind of thing. But, both of Hi-Rez’s other games are also getting the PS4 crossplay love.