Yes, that's fine. The non-English Stack Overflow sites even have a Help Center article about this. For example, the Spanish one:
Should I translate questions from English to Spanish?
Of course!
If you find a useful question on one of the sites of the Stack Exchange network (for example in Stack Overflow in English), which has not already been published in Stack Overflow in Spanish and the question is valid as described in What topics can I ask here?, please translate the question and the answer(s) to Spanish and publish it on the site. Our manifesto:
Create a world in which, for any query to a search engine, the search results show the link to a detailed answer in Spanish.
Translations increase the knowledge available in Spanish and help thousands of colleagues understand and solve problems currently limited by language.
(100% Google Translate, I'm surprised by its accuracy.)
Note that this is about cross-posting within the network; what you describe is another, less often seen form. In either case, it's probably a good idea to link the questions to each other (and if you copy a question from someone else, you are even required to provide attribution), and if any answers are posted, ask the author to post them on the other site as well or do it yourself (again keeping in mind the attribution rules).