The host Ashes broadcaster confirmed on its website that negotiations with the technology's Australian inventor, Warren Brennan, had broken down over the use of the infrared camera system.
The decision-review device, which uses heat sensors and infrared cameras to detect contact between the ball, bat and pads, will now not feature in the showpiece five-Test series, beginning at Brisbane's Gabba ground on November 21.
"It's their decision and that's what's been communicated to us. As far as I'm concerned, it is final," Brennan told Fairfax Media.
"We're just moving on with things. Channel Nine have got a new deal with Cricket Australia which I know has cost them a lot more money. I gather there had to be some restructuring of costs."
The development leaves the ball-tracking component, Eagle Eye, audio evidence picked up by stump microphones and slow-motion replays as the remaining tools at the disposal of the third official for decision reviews in the Ashes.
Trust in the Hot Spot technology was severely tested during the first leg of the back-to-back Ashes series won 3-0 by England in July-August.
While match umpires were criticised for poor decisions, Hot Spot was at the centre of a succession of contentious verdicts involving fine edges.
The dismissal of Australia's Usman Khawaja at Old Trafford even convinced Cricket Australia chief executive James Sutherland to seek clarification on it from the International Cricket Council (ICC).
In a dramatic lead-up to the fourth Test in Durham there were allegations, aired by Nine, that players were using silicon coating to limit the effectiveness of Hot Spot by hiding nicks.
The ICC's general manager of cricket Geoff Allardice cut short a holiday and went to Durham in England's northeast in an effort to restore players' confidence in the technology.
In response to the concern, the ICC last month announced it will be looking to improve both the Decision Review System and the training of umpires.
The ICC also announced that team's referrals would be topped-up to two reviews after 80 overs of an innings.
Currently, teams are only permitted a maximum of two unsuccessful reviews per innings, and the new playing conditions will be in force for next month's Ashes.
The cost of Hot Spot -- the company charges Aus$10,000 ($9,440) a day for the four-camera system Channel Nine has used, which would have cost Aus$250,000 ($236,000) for the Test series -- is a key reason behind the broadcaster cutting ties, but its poor performance in England is also understood to be a factor, Fairfax said.
A Cricket Australia spokesman said of the network's decision on Hot Spot: "We don't think it's appropriate to comment on discussions between Nine and one of its partners."