Socket compatible, yes.
The motherboard will be a bit factor though.
While the later revisions* of the GA-78LMT-USB3 can supposedly "handle" 125W CPUs, even then, they're not exactly stable.
Appropriate cooling for the VRMs is required if you want to run it without issues.
*And, if you have an early revision, it likely won't support it full stop.
It's worth noting the FX lineup is dated, and at this point "dead" (nothing better coming for it).
Even a budget Ryzen or Intel Sky or KabyLake would better the 8370 in most tasks.
Depending on your anticipated uses, Ryzen3 (launches at the end of the month, I believe) is a quad-core option...... Ryzen5 have 4 core/8 thread and 6 core/12 thread options that you should probably consider over the dated FX platform.