Enclose is the preferred spelling of the verb meaning to shut in, to surround, or to insert in the same envelope. Inclose was once an accepted variant, but it has faded out of use and now might be considered a misspelling of enclose. This extends to all derived words; enclosed, enclosing, and enclosure, are preferred to inclosed, inclosing, and inclosure.
The ngram below graphs the use of enclose and inclose in a large number English-language books published from 1800 to 2000. It shows that inclose was rather common two centuries ago but has steadily declined. Of course, the use of enclose has declined as well—perhaps corresponding to the rise of communication technologies making it unnecessary to enclose things within mailed packages—but it remains the prevalent spelling.
It’s still possible to find a few recent examples of inclose:
Each was charged with resisting arrest and remaining on inclosed land. [Herald Sun]
Visitors are to stay behind safety barriers in front of the animal’s inclosed cages. [KTEN]
In the midst of the city, within a vast inclosure girt by stout yellow ramparts, looms the House of the Lord. [The Atlantic]
But examples such as these are in much greater abundance:
In one corner of the courtyard, green-painted railings enclose the tomb of a saint. [Financial Times]
Altering and enclosing the veranda has provided a large space for a family corner and block area. [Manawatu Standard]
When the dogs are not racing or training they are each kept on a short chain, attached to their small enclosure. [NJ.com]