Note: Voicemail, Visual Voicemail, and Voicemail transcription are available from select carriers in select countries or regions.
Android phones can access voicemail by holding down the 1 key on the dial pad until the phone dials your 10-digit phone number. You will automatically connect to your mailbox and be prompted to enter your temporary password; this password is the last 4 digits of your phone number followed by the # key. Start the Google Voice app. Tap the three horizontal lines at the top left of the screen (sometimes called a hamburger menu), and then tap “Settings.” In the Voicemail section, tap “Voicemail greeting.” Tap “Record a greeting.” How do I access my voicemail? To call your voicemail on an Android phone, simply open your phone’s dial pad and hold your finger down on the “1” key. You can also call your voicemail from a different phone by calling your own number and tapping the pound key. How do you check your voicemail?

Also, carriers have a limit to how long they'll let you record a voice mail. Test it with your phone and a friend before you trust this method.
So far you probably had a generic voicemail greeting on your iPhone and want to change it to a personal voicemail greeting and with most carriers you don’t even need an additional voicemail recording app and can record a custom voicemail greeting directly on iPhone.