We say:
Having completed the work, I came back to home.
Instead of that can I say this?
I completed the work and came back to home.
Yes, you can say, but you don't use the preposition 'to' immediately in front of home. Home in the sentence is an adverb that means to or at the place you live.
You can also say:
When I finished the work, I came back home.
After finishing the work, I came back home.
After I (had) finished the work, I came back home.
Furthermore, when you use home as a noun, you can use the to in the following way;
He has no home to go to.
He went back to his home.
But "He went back to his house" is preferable.