There's a lot of info on the web, but I never can find a complete canonical way of doing this when I need it, so here's mine:

On the source machine, dpkg --get-selections > my-selections (here, everybody agrees though)

On the target machine:

# apt update
# apt-cache dumpavail | dpkg --merge-avail
# dpkg --clear-selections  # that's dangerous if you don't set reasonable selections afterwards!
# dpkg --set-selections < my-selections
# apt-get -u dselect-upgrade

And voila.