Automation Testing with Java, how to combine web and mobile tests for a website?

I work with Selenium. For this moment I have a ready testing framework written with TestNg. The testable product is a website. Now I need to have tests for mobile platforms.(I've started with Appium already). But the question is how can I handle the test execution to run for both web and mobile platforms before deployment? Also,is it possible to reuse my test codes written for the web (to "import" to mobile tests' methods)?

Thank You for any help and advice !