Early Tuesday morning, somebody at Apple’s iTunes Store flicked a switch and six of HBO’s most popular series became available for download for prices ranging from $1.99 to $2.99 per episode. They are:

• Sex and the City: $1.99 per episode
• The Wire: $1.99
• Deadwood: $2.99
• Flight of the Conchords: $1.99
• Rome: $2.99
• The Sopranos: $2.99

As widely reported on Monday, the deal is a breakthrough for both Apple (AAPL) and Time Warner’s (TWX) HBO.

For HBO, which is making individual episodes available for the first time, it’s a chance to expand viewership beyond its 30 million cable TV subscribers to Apple’s broader audience of 50 million registered iTunes users.

For Apple, it’s a strong signal that Steve Jobs has backed away from his stubborn insistence on flat-rate pricing — $1.99 for TV episodes, $.99 for songs — and is ready start a new round of deal making in Hollywood.

On May 1, Apple announced an agreement with Warner Brothers, 20th Century Fox (NWS), Walt Disney , Paramount , Sony and others to make movies available for iTunes download the same day they are released on DVD at two price points: $14.99 for new releases and $9.99 for older films. (see Apple’s new Hollywood deal)

Could a rapprochement with NBC — which pulled its series off iTunes last December in a dispute over flat rate pricing (see here) — be far behind? The fact that NBC (GE) started streaming free episodes of two of its most popular shows, The Office and 30 Rock, to iPhones last week seems like a promising sign.

[UPDATE: Apple posted a press release this morning. HBO is “excited.” Apple is “thrilled.”]