As described by the linked Stackoverflow answer, run these commands:

sudo add-apt-repository ppa:git-core/ppa -y
sudo apt-get update
sudo apt-get install git
git --version

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This will get you Git 2.6.4 (as of Dec 2015).

Troubleshooting

If you don't have add-apt-repository yet, install it with:

sudo apt-get install python-software-properties software-properties-common