Pioneering consumer Internet phone (VoIP) service provider Skype is available on the iPhone today.

“The number-one request we get from customers is to make Skype available on iPhone. There’s a pent-up demand,” Skype CEP Scott Durchslag told Reuters news service at the CTIA annual mobile showcase in Las Vegas.

Skype already offers versions of its service for Nokia, Windows Mobile and Android-based phones.

Skype’s new iPhone app is free to download and calls between Skype users will be free. As with Skype’s services on other platforms, there will be a charge to connect calls to numbers outside of the Skype network.

iPhone Skype will also work on the latest iPod Touch, which has a WiFi connection and a microphone.

Skype is scheduled to come to the BlackBerry in May.