Former Boro midfielder Hignett resigned at Victoria Park on Monday evening and Pools confirmed in a brief statement that the 44-year-old would not be working his notice period with the club.
Pools boss Colin Cooper is now in the hunt for a new assistant - former team-mate Neil Maddison and ex-Boro assistant boss Mark Venus have been linked with the job - while Hignett took up his new post at the Riverside on Tuesday.
"It was a tough decision to go, a really tough decision, and a wrench to leave Coops," Hignett told the Hartlepool Mail. "But it was too good an opportunity to turn down.
"I have left on fantastic terms with Colin, he understood the situation completely and I have his full support.
"Obviously he was disappointed, but he understands the opportunity that I've been given and so did (chief executive) Russ (Green) and the chairman (Ken Hodcroft) to be honest.
"I parted on good terms with everybody. I have met some fantastic people at the club and I will miss them."
Hignett said his departure would not affect his friendship with Cooper.
"They are lucky to have Colin," He added. "I have no doubt at all he will go on to bigger things in his managerial career."