Using kdiff3 as default git diff viewer on Mac OS

I have kdiff3 installed on my Mac (Version 0.9.97, 64 bit). Here's my ~/.gitconfig:

[filter "media"]
    required = true
    clean = git media clean %f
    smudge = git media smudge %f
[user]
    name = My Name
    email = me@example.com

[core]
    editor = atom --wait
[merge]
    tool = kdiff3
[mergetool "kdiff3"]
    path = /Applications/http://ift.tt/1za3pO5
[diff]
    tool = kdiff3
[difftool "kdiff3"]
    path = /Applications/http://ift.tt/1za3pO5

Everything seems to be fine, except for the fact that when I do git diff, I see the output of the console diff. Any ideas on how to solve this?