Android: Background Image Size (in Pixel) which Support All Devices

The following are the best dimensions for the app to run in all devices. For understanding multiple supporting screens you have to read http://developer.android.com/guide/practices/screens_support.html

xxxhdpi: 1280x1920 px
xxhdpi: 960x1600 px
xhdpi: 640x960 px
hdpi: 480x800 px
mdpi: 320x480 px
ldpi: 240x320 px

Android Devices Matrices

                            ldpi     mdpi     hdpi    xhdpi    xxhdpi      xxxhdpi
Launcher And Home           36*36    48*48   72*72    96*96    144*144     192*192
Toolbar And Tab             24*24    32*32   48*48    64*64    96*96       128*128
Notification                18*18    24*24   36*36    48*48    72*72       96*96 
Background                 240*320  320*480 480*800  768*1280  1080 *1920  1440*2560 

(For good approach minus Toolbar Size From total height of Background Screen and then Design Graphics of Screens )

For More Help (This link includes tablets also):

https://design.google.com/devices/

Android Native Icons (Recommended) You can change color of these icons programmatically. https://design.google.com/icons/

Check this. This image will show for all icon size for different screen sizes

I looked around the internet for correct dimensions for these densities for square images, but couldn't find anything reliable.

If it's any consolation, referring to Veerababu Medisetti's answer I used these dimensions for SQUARES :)

xxxhdpi: 1280x1280 px
xxhdpi: 960x960 px
xhdpi: 640x640 px
hdpi: 480x480 px
mdpi: 320x320 px
ldpi: 240x240 px

GIMP tool is exactly what you need to create the images for different pixel resolution devices.

Follow these steps:

1. Open the existing image in GIMP tool.
2. Go to "Image" menu, and select "Scale Image..."

3. Use below pixel dimension that you need:

   xxxhdpi: 1280x1920 px

   xxhdpi: 960x1600 px

   xhdpi: 640x960 px

   hdpi: 480x800 px

   mdpi: 320x480 px

   ldpi: 240x320 px

4. Then "Export" the image from "File" menu.