With both AT&T and Verizon selling Samsung devices that come with locked bootloaders out of the box it was only a matter of time until an exploit was found to get the Samsung devices rooted!
Thanks to the famous Geohot he has found a hole within the Android kernel that allows many Android devices to be rooted within only a few minutes with no computer required!
This root guide will work with:
AT&T Galaxy S5 SM-G900A
AT&T Galaxy Note 3 SM-N900A
AT&T Galaxy S4 SGH-i337
AT&T Galaxy S4 Active
Verizon Galaxy S5 SM-G900V
Verizon Galaxy Note 3 SM-N900V
Verizon Galaxy S4 SCH-I545
& many other devices! People have reported this method also works on Asus, Sony, and other Android devices as well!
Users have also confirmed that this does NOT trip Samsung KNOX!
Follow this guide below to root the AT&T/Verizon Galaxy S5, Note 3, Galaxy S4, and Galaxy S4 Active.
1. Go into Settings > Security > and check mark "Unknown sources".
2. Download tr.apk directly to your phone using the download link below.
Download tr.apk
3. Up in the notifications of your phone tap on the "tr.apk". This file is also located in your "Download" folder.
4. After the towelroot pops up tap on "Install".
5. Now tap on "Open".
6. Select "make it ra1n".
7. After 15 seconds your phone will reboot and you will be rooted. If you want to check that your rooted you can install an app like Root Checker to confirm that.
Credits - XDA