Also use --execute to get the output
jupyter nbconvert --execute --to html notebook.ipynb
This produces a notebook.html file.
The best practice is to keep the output out of the notebook for version control, see: Using IPython notebooks under version control
But then, if you don’t pass --execute, the output won’t be present in the HTML, see also: How to run an .ipynb Jupyter Notebook from terminal?
For an HTML fragment without header: How to export an IPython notebook to HTML for a blog post?
Tested in Jupyter 4.4.0.