The 37-year-old, who also followed Lampard to Everton, has unsurprisingly looked to his former employers when assembling his backroom team, with Andy Myers arriving at Millwall as his assistant. Myers was in charge of Chelsea's U21 side last term, before moving into a role with the loan department this season.
Edwards has left his position as England U20 head coach to become the new permanent boss at The Den, replacing Gary Rowett who left the club by mutual consent last month.
"Firstly, it's a really proud day for me and my family," Edwards told the club's official website.
"Although I have been coaching for a long time, a lot of people will be aware that this is my first job managing as Head Coach.
"Throughout the years, at various levels, you think you would like to have the opportunity to make the step up. To do it at a club like this, to be Head Coach of Millwall Football Club - I don't take that lightly at all. I'm really excited."
Edwards will take charge of training at the club for the first time on Tuesday, building up to his first match in the dugout on Saturday when Millwall travel to face Sheffield Wednesday. Adam Barrett, who has been leading the side as caretaker manager since Rowett's departure, will be part of Edwards' backroom staff, as will goalkeeper coach Andy Marshall.
Millwall currently sit 18th in the Championship table, having won just two of their last ten matches.
Chairman James Berylson said: "With Joe, I'm excited. He is somebody who I think is very innovative and has some positive ideas about the progression we can make as a club.
"It was a thorough process, with no stone left unturned, and Joe was engaging, attentive, and impressive throughout, and I felt that we could have a productive working relationship together.
"We welcome both Joe and Andy to The Den with open arms and look forward to seeing the impact they can make on and off the pitch throughout what we hope to be a long relationship with Millwall."