Lomas leaves a successful 18-month spell in Perth and the Scottish Premier League with St Johnstone to take over at The Den.
Speaking about his new position, he said: "This is a really exciting challenge for me and I can't wait to get stuck into it.
"I know Millwall well as a club. It has a great set up and passionate loyal fans who, if we can get them on our side, particularly at The Den, will be a real asset to us.
"There is already a nucleus of a good squad there, with the likes of David Forde, Paul Robinson, Alan Dunne, Danny Shittu and Jimmy Abdou, proper players and good characters, and those are the sort of people we need and the Millwall fans respond to.
"I know there is a good group, but we will need to add four or five, particularly in attacking areas and then I think we'll be ready to give it a real go. In making signings I will be looking for character and the right type of player as well as ability.
"The Championship is a great league, exciting, very competitive, passionate, full-on and while we'll be underdogs against many of the clubs we face, that's the way I like it.
"Our first priority is to turn the recent home form around. I found the same when I arrived at St Johnstone - good away, less so at home and we worked to get that right. That's my number one goal again now.
"Millwall is a family club, a working class club whose fans hold it very dear to their hearts. I've already been asked, what's an ex-Hammer doing managing them, then?
"The answer is that I was a council estate kid, I love a challenge, I like hard work and I understand the fans who work hard all week and come to see Millwall on a Saturday expecting to see their team play with pride and passion.
"I am grateful for the responsibility of helping deliver that for them. For those who have their doubts, it is up to me to show by my actions, and more importantly, by our results, that they can believe in me."