Install and configure toggl-cli. Add main command to your path as toggl
And add this it to your Taskwarrior hooks:
mkdir -p ~/.task/hooks ln -s `pwd`/on-modify.toggl ~/.task/hooks/on-modify.toggl
Use task <TASK ID> start and task <TASK ID> stop to record when you have
started and stopped working on tasks.
Tasks will appear in your toggl automatically.