The judiciary panel of Bob Lindner, Mal Cochrane and Don McKinnon took just three minutes to reach their verdict after a hearing that lasted an hour and a half.
The Melbourne prop is free to play in Friday's round-21 fixture against Wests Tigers at Leichhardt Oval.
"I'm just relieved to get the result," Bromwich said after the verdict was read out.
"I'm happy they gave me a fair hearing. I never felt guilty and I will move forward to this Friday night."
The panel accepted Bromwich's version of events over the incident in the 69th minute of the Storm's clash with St George Illawarra on Saturday at Napier.
In giving evidence, the Kiwi international asserted he was having trouble breathing as a result of a medical condition, as Dugan wrapped his right arm around Bromwich's face while he lay on the ground.
According to a medical report tendered to the hearing, Bromwich had surgery on a broken nose on June 30, which left him breathing with difficulty through his nose, especially when he was tired.
Bromwich asserted any pressure Dugan felt on his biceps was him attempting to breathe.
"I definitely didn't bite him," Bromwich told the hearing.
"I have been playing rugby league for a long time and I have never bitten anyone before. I play the game hard but fair and biting is just dirty. I don't know what he felt but I didn't bite him."
In giving evidence, Dugan admitted he was doing "ground work", or wrestling, on Bromwich in a bid to slow down the Kiwi international's play the ball. However, he was adamant Bromwich bit him.
"I know what a bite feels like," Dugan said.
Dugan reeled out of the tackle visibly irate and, in the following few tackles, repeatedly attempted to gain the attention of referee Matt Cecchin to alert him of his concerns he had been bitten.
The NSW fullback said he could see "a red mark, an outline of saliva, an outline of the mouth" on his arm.
However, in his match report, Cecchin said: "I didn't see any mark, which could be due to the player's tattoos".
Bromwich's defence counsel Nick Ghabar seized on Cecchin's remarks in his closing statement and on Dugan's evidence that the Storm star perhaps couldn't breathe.
Cecchin said the evidence was "inconclusive" and, as such, the panel couldn't find his client guilty.
Prosecutor Peter McGrath's claims that it was "not an extravagant bite", but a bite nonetheless, were dismissed by the panel.
