Yes, but this only saves you the work of modeling (with two exceptions)
The process is exactly the same as modeling your own character and rigging it. If you need an explanation of that, you can google around for some tutorials on how to do that.
If you already have another skeleton, you might save some work if and only if
- The joints are in the correct place on the Armature
- The vertex groups on your model are preserved on your mesh, and match the names of the bones of said skeleton
If you don't have the vertex groups, you will need to weight paint them on as you would any character rig.
Because you mentioned Unity, I would be remiss to mention that Unity has a concept called Model Avatars . Basically, this is a way to tell Unity that a model is sharing a Armature rig, and that concepts can be shared across models.
When importing a model, you can generate an Avatar or use a pre-existing one. You can share assets for the armature of the original Avatar (such as poses and animations) to the new model, if they share avatars.
Unity has rules for what can have shared Avatars, please look to Unity's Documentation for that.