The date was given in a series of TV adverts broadcast on Sunday, and was later confirmed by a spokesman for the California-based company.
The device, which combines the features of a mobile phone and personal digital assistant, will sell for $499 (£251) and $599, depending on configuration.
The phone's much-touted feature is a completely touch-sensitive interface.
The adverts on sunday showed off several of the gadget's features, including surfing the net, watching videos and scrolling through e-mails using a finger as a pointer.
They ended with the news that the phone would be available "Only on the new AT&T" and "Coming June 29".
The product is one of the most highly-anticipated devices ever made by Apple and was announced last January at MacWorld in San Francisco by the firm's chief executive Steve Jobs.
His unveiling of the device managed to overshadow one of the world's largest technology conferences, CES, which was being held at the same time in Las Vegas.
Apple hopes to grab a slice of the global mobile phone market, which dwarfs the market for MP3 players, of which it is the dominant player with the iPod.
It hopes that the phone's multi-touch display, and ability to work with its iTunes music and video store, will make the device attractive to consumers.
A release date for Europe and the rest of the world has not been given.