The former Shildon boss left his role at Dean Street on Wednesday morning less than 24 hours after his side had lost their Northern Premier League East play-off semi-final at Marske United.
Moore had led the Railwaymen to the Cleator Cup, Durham Challenge Cup and a first ever promotion into the Northern Premier League during his five-year managerial reign.
He will now begin planning for his first season in charge of Hebburn and will be joined by Shildon assistant Mark Hudson and goalkeeper coach Carl Morris after the duo agreed to follow Moore to the Green Energy Sports Ground.
Former Hebburn joint-caretaker manager Simon Harris will form part of Moore’s backroom staff but Chris Errington and strength and conditioning coach Ben Sherwood will both depart.
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Hornets chairman Vin Pearson revealed the reasons behind the move to appointment Moore and the timing of the decision.
He said: “We are thrilled to have Bobby (Daniel) on board as our new first-team manager.
“We obviously knew about his achievements at Shildon - as soon as he made us aware of his interest, hearing how ambitious he is and how his beliefs and objectives align to ours, it made the acquisition an appealing one.
“We obviously wanted to be respectful to fellow Northern Premier League club Shildon and allow Bobby time to discuss his situation with them, and agreed we were happy to wait until the end of the 2021/22 season for him to come on board.
“I think he'll kick our club on and we're looking forward to working with him.”
Moore will hope to replicate the success he achieved at Shildon as he moves on to the second managerial role after learning his trade at Dean Street.
The former Mansfield Town and Spennymoor Town described himself as “grateful” to have been handed a chance to succeed FA Vase and promotion-winning manager Kevin Bolam and is ready for the challenge.
“I'm excited," he explained.
“I've went from a great club in Shildon, to another which has ambition to compete in the league.
“I'm grateful that the club have chosen me, and I want to do my best for the football club.”