How do I change the default shell used in Byobu (tmux)?

Put the following in your $HOME/.byobu/.tmux.conf:

set -g default-shell /usr/bin/zsh
set -g default-command /usr/bin/zsh

Full disclosure: I'm the author and maintainer of Byobu.

For me, Dustin's solution didn't seem to take at first.
If anyone is in the same boat, you might want to read this.
I used to have a working setup where gnome-terminal launched zsh as a login shell, which then launched byobu with my window (split) setup and a couple of zsh instances in there. After a distro reinstall, the shell instances in the splits were suddenly bash, for whatever reason, even with the above fix.
Whenever I launched zsh in those splits I'd get a message from oh-my-zsh that a plugin was missing.
I installed the missing package for the plugin and configured it correctly, and now all stages of the setup execute correctly. I suspect that the error message from the sourcing process whithin oh-my-zsh may have caused a fallback to bash (possibly within tmux?).