The Championship side sacked Gary Rowett last month and Barrett was handed the caretaker manager’s role temporarily.
Barrett joined Millwall back in 2017 as a first-team development coach and now he is set to become a member of Edwards’ backroom staff.
Aldridge insists that Barrett has been a valuable member of the club since he joined and he has done a commendable job as the caretaker boss.
He revealed that Barrett is staying with the Lions because he wants to stay and the new boss Edwards also wants him to stay.
“Adam has been a huge part of that and his quality of work is excellent”, Aldridge told the South London Press.
“He is an outstanding person.
“He is hugely well-respected and liked by the players and staff.
“He stepped up as a caretaker in quite difficult circumstances.
“It wasn’t exactly a kind run of fixtures and we had some injury problems.
“In terms of performance, the feeling around the training ground and squad he led the group fantastically well during what is obviously an uncertain period, by the nature of it.
“Adam has stayed because – A – he wanted to stay and – B – because Joe wanted him to stay.
“That is absolutely essential that it was a dynamic that was felt on both sides.”
Barrett, 43, finished his playing career at Southend United after turning out for Crystal Palace, AFC Bournemouth, Plymouth Argyle and Bristol Rovers.
