Staunton, who has managed the Republic Of Ireland national team had been with another former Sky Blue Gary McAlliister at Leeds United until they were sacked last December.
The pair's first game in charge will not be the JPT game at Leeds but a league match against Dagenham & Redbridge on Saturday.
Darlington chairman Raj Singh said to his club's website: "We're excited about the prospect of working with someone with vast experience in the game and a wealth of contacts. Steve enjoyed a formidable playing career and he has a strong desire to succeed as a manager as well.
"We spoke to a handful of applicants over the weekend and Steve came across as the most professional and organised. He had done some thorough homework on Darlington and League Two, our players and potential new players, some of whom he's already targeted to bring in.
"He's extremely realistic and is aware of the situation here at Darlington,
but he's confident he can utilise his contacts to bring players in who will
improve our squad."