Samsung recently started rolling out its official Android 4.1.2 Jelly Bean firmware update for the Samsung Galaxy S2 bearing model number GT-I9100 in several countries. The new official firmware is now available for download through Samsung KIES as well as Over-The-Air (OTA) update.
Samsung Galaxy S2 I9100 users who have already updated their devices with Android 4.1.2 Jelly Bean, may root their devices using the tutorial below.
Disclaimer: Rooting voids the warranty of your device. We and the developer of this rooting procedures shall not be held responsible if any undesirable outcomes may happen to your device. use of this root guide is solely at your own risk!
Pre-requisites
1) Install USB Driver for Samsung Galaxy S2 on the computer.
2) Enable USB Debugging Mode on the phone.
3) Make a backup of all your important data before following the guide.
4) The Galaxy S2 should be factory unlocked and not locked to any particular carrier.
5) Ensure the battery of the phone is charged more than 80 per cent.
6) The Root Kernel file works only on Samsung Galaxy S2 I9100 running on Android 4.1.2 Jelly Bean firmware. Applying this on any incorrect variant will brick the device. Verify the model number of the Galaxy S2 by navigating to Settings >> About Phone.

File Required
1. Root Kernel for Galaxy S2 I9100: Siyah-s2-v6.0b4.tar or Siyah-s2-v6.0b5.tar
2. Odin 3.07

Steps to Root Galaxy S2 I9100 Running on Android 4.1.2 Jelly Bean Firmware
Step 1: Extract Odin 3.07 file using winrar/7zip/winzip or any other extracting tool.
Step 2: Switch off the Galaxy S2. Then boot the device into Download Mode by pressing and holding Volume Down + Home buttons together and then press the Power button until the device turns on. Now press the Volume Up button to enter Download Mode.
Step 3: Launch Odin on the computer.
Step 4: Connect the Galaxy S2 to the computer using USB cable while it is in the Download Mode. Wait until Odin detects the device. When the device is connected successfully, the ID: COM box will turn yellow with the COM port number. Additionally, the successful connected will be indicated by a message saying Added. If Odin fails to detect the device then re-install USB driver.
Step 5: In Odin, click the PDA button and select the Root Kernel file.
Step 6: Verify that Auto Reboot and F.Reset Time checkboxes are selected in Odin. Also, ensure the Re-Partition option in Odin is not selected.
Step 7: Double-check and click Start in Odin. The installation process will now begin.
Step 8: Once flashing completed, your phone will restart and soon you will see a PASS message with green background in the left-most box at the very top of the Odin. You can now unplug the USB cable to disconnect your device from computer.

Samsung Galaxy S2 I9100 running on Android 4.1.2 Jelly Bean firmware is now rooted successfully. You may now install any app that requires root permission.

Thank's to all fellas at XDA who first tried out this rooting technique. This root method was originally posted via XDA-Developers.

Samsung has released another official Android 4.1.2 Jelly Bean firmware update with firmware build number I9100XWLSW for Samsung Galaxy S2 GT-I9100 users in United Kingdom / Ireland. The new official firmware reportedly brings a host of bug-fixes and feature enhancements over its previous build.
Firmware details
PDA: I9100XWLSW
CSC: I9100XEULS5
MODEM: I9100XXMS2
Version: Android 4.1.2
Built date: May, 2013
Regions: United Kingdom / Ireland
The official firmware is now available for download via Over-The-Air (OTA) update as well as through Samsung KIES. However, those who fail to upgrade their devices with Android 4.1.2 XWLSW Jelly Bean via official method, may follow our step-by-step guide to install the update manually.
Pre-requisites
1. Install USB Driver for Galaxy S2 on the computer.
2. Enable USB Debugging Mode on the phone by navigating to Settings >> Developer Options (Android 4.0 or later) or go to Settings >> Applications >> Development (Android 2.3 or earlier).
3. Make a backup of all your important data before following the guide.
4. The Galaxy S2 should be factory unlocked and not locked to any particular carrier.
5. Ensure the battery of the phone is charged more than 80 per cent.
6. The Android 4.1.2 XWLSW Jelly Bean firmware is compatible only with Samsung Galaxy S2 I9100. Applying this to any incorrect variant might brick the device. Verify the model number of the Galaxy S2 by navigating to Settings >> About Phone.
Files Required
1. Android 4.1.2 XWLSW Jelly Bean Firmware (Mirror Link 1, Link 2) for Galaxy S2 I9100
2. Odin 3.07 (Mirror Link)
Steps to Update Galaxy S2 I9100 with Android 4.1.2 XWLSW Jelly Bean Firmware
Step 1: Extract Firmware zip file that you downloaded already from above link using WinRAR/7-Zip/WinZip or any other extracting tool, you will get a .tar.md5 file and some other files.
Step 2: Extract Odin zip file and you will get Odin3 v3.07.exe along with few other files.
Step 3: Power off your phone. Wait 5-6 seconds for vibration to confirm complete switch off.
Step 4: Boot the device into Download Mode by pressing and holding Volume Down + Home buttons together and then press the Power button until the device turns on. Now press the Volume Up button to enter Download Mode.
Step 5: Run Odin on the computer as an Administrator.
Step 6: Connect the Galaxy S2 to the computer using USB cable while it is in the Download Mode. Wait until Odin detects the device. When the device is connected successfully, the ID: COM box will turn yellow with the COM port number. Additionally, the successful connected will be indicated by a message saying Added. If Odin fails to detect the device then re-install USB driver.
Step 7: Choose the following files in Odin from extracted I9100XWLSW firmware folder by using respective checkboxes:

• Select the PDA checkbox, and choose the file named .tar or .md5.
• Click the Phone checkbox, and choose the file with 'modem' in its name (ignore if there is no such file)
• Click the CSC checkbox, and select the file with 'csc' in its name (ignore if such file is missing)
• Choose the PIT checkbox, and choose the .pit file. Use only the file obtained during extracting in step 1 above, otherwise ignore it.

Step 8: In Odin, enable Auto Reboot and F. Reset Time checkboxes. Also, ensure the Re-Partition checkbox is chosen only if a .pit file was chosen in the previous step.
Step 9: Verify everything suggested in Step 7 and Step 8 is done correctly. Then hit the START button to begin the flashing process.
Step 10: Once flashing completed, your phone will restart and soon you will see a PASS message with green background in the left-most box at the very top of the Odin. You can now unplug the USB cable to disconnect your device from computer.
Samsung Galaxy S2 I9100 should be now updated with official Android 4.1.2 XWLSW Jelly Bean firmware. Head over to Settings >> About Phone to verify the software version running on the device.
Note: If  Galaxy S2 I9100 stuck at booting animation after Step 10 then go to recovery mode (press and hold the Volume Up, Home and Power buttons together) and perform Wipe data/Factory Reset and Wipe Cache Partition task before selecting reboot system now function. In recovery mode use Volume keys to navigate between options and Power key to select the option. Please note, performing wiping task will erase your device internal memory data and not external SD card data.
Click here to know How to Root Galaxy S2 I9100 running on Android 4.1.2 Jelly Bean firmware.