PlayStation Europe community manager Chris Owen announced on Twitter that the change would be coming tomorrow, March 12, when Home version 1.86 goes live.
The Trophy integration will be worldwide, and applied retroactively. Details on what ones will be available will be announced tomorrow.
First launched in 2008, this is the only update PS Home has received in some time. We still don't know quite what's planned for it in the future, and there's been no announcement regarding whether or not it'll come to PS4.