Holloway was appointed as Steve Lomas' successor on Monday and took his first training session on Tuesday.
The 50-year-old former QPR and Crystal Palace boss is "honoured" to have been given the role and said he has "never felt more wanted" by a club's board.
"I'm delighted to be here," Holloway told the club's official website. "I was out of work and got a phone call from a fantastic friend of mine in Kenny Jackett. He recommended that I speak to (chief executive) Andy Ambler and (chairman) John Berylson. I asked him why, and he told me what kind of people they are.
"I met Andy on Thursday and John on Friday, and I was completely blown away for lots of reasons. Everything they want for the club completely mirrored how I feel. I've never felt so wanted in my whole life."
Millwall are fourth from bottom of the Championship and face a trip to Huddersfield on Saturday.