I created custom fields for standard objects(contact and lead), added that fields to page layout and included page layout in managed package. How to make change of page layout assignment when package is installed to other org?
Vladyslav, you cannot automatically assign Page Layouts in a managed package. This is normally left to the installer.
There is a good reason for this, as most clients wouldn't want a package overriding their own preferences with their layout.
My recommendation is to provide a Post Install VF page (or URL) where the user can learn how to replace the Page Layout, or how to add your fields to their existing layout.