4J Studios developed the Xbox 360, Xbox One, PlayStation 3, PlayStation 4, and PlayStation Vita versions of Minecraft for Mojang.
The Dundee-based Scottish developer became especially known for adapting Minecraft from its computer origins to console and handheld platforms. Its first Minecraft console release was Minecraft: Xbox 360 Edition, launched through Xbox Live Arcade on May 9, 2012. The port added features suited to consoles, including a redesigned crafting interface, tutorials, split-screen multiplayer, and online play.
4J Studios subsequently handled the Xbox One Edition and the PlayStation 3, PlayStation 4, and PlayStation Vita Editions. These releases were distinct from the later Bedrock Edition, which unified Minecraft across many platforms and enabled broader cross-platform play. The older console releases are now generally called Legacy Console Editions.
Mojang created Minecraft, while Microsoft acquired Mojang in 2014. That ownership change can cause confusion, but it does not change the answer to this question: 4J Studios was the specialist developer responsible for these console ports.