Voicemail generates an SMS Message

Why is my voicemail generating SMS messages with a transcript of the voicemail with the phone number of the caller and the message "Depositing new message <followed by text transcription of the message>. To be clear, this is NOT the feature of visual voicemail in the voicemail screen. That is happening normally and working fine also. This is a separate text message being delivered to my phone as soon as the voicemail is left from the person who left the message. HOW CAN I TURN THIS OFF? IS THIS A CARRIER SETTING OR AN IPHONE SETTING FOR VOICEMAIL OR MESSAGES OR CELLULAR?