While lhunath’s answer pushed me in the right direction, zsh does not seem to source .profile automatically. Lot’s of good info on this topic can be found on this superuser post.
The adaption I’m using is putting common aliases and functions in .profile and manually sourcing them as follows:
In ~/.bashrc:
source ~/.profile
In ~/.zshrc:
[[ -e ~/.profile ]] && emulate sh -c 'source ~/.profile'
emulate is a zsh builtin command. With single argument set up zsh options to emulate the specified shell as much as possible.