how do i transfer my mail account from my old mac to my new mac

I just bought a new Macbook Pro and I have a six-year-old Macbook Pro. I want to directly transfer my mail from my old Mac to my new one. The problem is that I have never figured out how to completely sync my gmail account with what is on my old Mac, so my Gmail account hasn't been touched in years and I have worked with my email strictly through my Mac mailbox, so I can't just sync the new mail with Gmail. How can I sync my new mail to the one on my old Mac (and maybe even sync my Gmail account with my Mail)?