The issue of not receiving messages when switching from iPhone to Android has something to do with the iMessage system. This causes the messages for your number to go through the Apple servers prior to your phone.
So switching to non-Apple phones needs disabling of iMessage so that messages will be delivered to your phone without passing through Apple servers. Phandroid provided the steps below:
1. Disable iMessage With an iPhone
Using your old iPhone and disable iMessage is the easiest way to do with few settings as follows: Settings -> Message -> iMessage then Off.
2. Sign Out Your Account
An alternate solution if you have no iOS device and want to unlink from iMessage completely is to sign out your account. Go to Settings app -> Messages -> Send and Receive -> Apple ID -> Sign Out. This one should solve the problem. Take note changes will take effect after a day or two. When still unresolved, you can try other options.
3. Using an iPad or any iOS Device to Disable iMessage
If there is an available iPad, you can also disable iMessage from it. The same applies as in option# 1: Settings -> Message -> iMessage then Off. But if you want to continue iMessage on your iPad or other iOS device, do not turn off the message completely. All you need is to delink the number from the device: Settings -> Messages -> Send & Receive -> You can be reached by iMessage at -> Go to the number you use -> Uncheck the number.
4. Disable iMessage in Mac
If you are using iMessage on your Mac with a phone number that is linked, you need to deactivate the service again. Go to Messages -> Preferences -> Accounts tab -> You can be reached for messages at -> Look for your phone number -> Uncheck.
5. Unregister Your iPhone
If the above did not help, unregistering your iPhone might work. Be warned that this can affect your terms of warranty services like Apple Care. You can do this by going into Apple's site. Go to My Support Profile -> Click "X" next to your iPhone.
6. Factory Reset And Erasing Data
If problem persists despite the methods used above, you may resort to perform factory reset and data wipe which should delink your number from iMessage successfully. Take note that this procedure is irreversible so it is important to backup your data.
First, backup your current settings and data with iTunes or iCloud by connecting your iOS unit to a computer or enable iCloud Backup. Go to Settings -> iCloud -> Storage and Backup -> iCloud Backup. If you plan to reset or erase your device that runs iOS 7 or higher, you need to disable Find My iPhone by: Settings -> iCloud -> Find my iPhone.
Now to do the factory reset and erase proper, you can do so with the iOS device. No need to connect to a computer. Go to Settings -> General -> Reset -> Erase all Content and Settings -> Erase iPhone -> Erase iPhone.
7. Call Apple
If all the methods above did not work, your last option is to call Apple. Its support line is 1-800-MY-APPLE. Your request is for them to disable your iMessage manually. Have your basic information handy like your Apple ID, password and the phone number. Changes could still take some days to take effect.