I know this is an old thread but I tried the suggested answers and unfortunately simply replacing line breaks with <br /> didn't do what I needed it to. It simply rendered them literally as text.
One solution would have been to disable autoescape like this: {% autoescape false %}{{ mystring }}{% endautoescape %} and this works fine but this is no good if you have user-provided content. So this was also not a solution for me.
So this is what I used:
In Python:
newvar = mystring.split('\n')
And then, passing newvar into my Jinja template:
{% for line in newvar %}
<br />{{ line }}
{% endfor %}