How to migrate from string column to foreign key pointing to row in other table with same string value in Laravel?

I am using Laravel and need some help migrating a column from a populated table preserving the content logic. There is a table pages with a column named icon that accepts string values.

Ex:

Schema::create('pages', function (Blueprint $table) {
        $table->increments('id');
        ...
        $table->string('icon')->nullable();
}

The pages table is populated and the icon column, being nullable, is not always used.

A new icons table was created to store all the usable icon classes.

Ex:

Schema::create('icons', function (Blueprint $table) {
        $table->increments('id');
        $table->string('name');
});

How can i migrate the icon column from the pages table to be a foreign key that points to the icons table row that has the same value in the name column or null if not populated?

via Chebli Mohamed