Both the platforms will get a dedicated app, which will resides on your PC and give you access to many things. For Android users the Cortana companion will be available in late June and iOS later this year.
Cortana for Android or iOS won’t work same as we’ve seen in Windows Phones, due to various integrations. There will be certain things that Cortana does on Windows Phones that won’t work on either of these platforms. But still you’ll get notification support and most of the features of Cortana that currently exist in Windows.