Theres 3 ways you can go about this.

• Boolean. It works, but its a nightmare to deal with, and leads to N-gon disasters. Though if you keep it as a modifier, it should look decent.
• Manual joining. Probably the best looking, and (second) easiest to work with. But takes a bit of work, and modelling skills. And a backup of the model incase you fuck something up beyond repair.
• Data transfer. This is a neat little method of 'joining' objects together with modifiers, that looks beautiful, and keeps objects separated. Though it takes some prep work, and also would recommend a backup of the mesh to preserve the original incase it doesnt work out.