The 2005 Sydney premiership coach has been out of senior coaching for the past three seasons since stepping down from the Swans at the end of 2010.
Roos led the Swans to seven finals appearances in his eight full seasons.
His appointment is a huge coup for the Demons, who sacked Mark Neeld as coach midway through 2013, also churned through a chief executive and a chairman, and won just two matches for the year to finish second-bottom.
Roos, 50, also had a stellar playing career, featuring in 356 matches for Fitzroy and the Swans.
"We're absolutely delighted Paul has agreed to this role for at least the next two years," Demons chairman Glen Bartlett said.
"His appointment is the most significant news for this club for a very long time."
Roos' contract is for two years, with a one-year option.
Roos said he had initially not been interested in returning to senior coaching when new Demons chief executive Peter Jackson spoke to him 12 weeks ago.
But his mood changed when Jackson put to him the prospect of being the senior coach, with a firm succession plan in which an upwardly mobile assistant would eventually take over.
"One of the turning points was when Peter came to me and asked 'would you be interested in heading the organisation, then handing it over to someone else?'" Roos said.
"That really sparked the interest. I'm extremely, extremely excited about being introduced as the Melbourne coach.
"I'm really looking forward to setting a direction for the players and the football club, and setting some really high standards."
A similar succession plan took place at Sydney when Roos stepped down and was replaced by senior assistant John Longmire.
Longmire guided the Swans to the premiership last season.
Roos met senior club players last week and came away impressed - no one underestimating the task which lies ahead of the club to become competitive.
But he said the Demons were better than they'd showed in 2013, especially avoiding the blowouts which had characterised their season.
"They're certainly not sugar-coating it - I know what I'm coming into. I know it's going to be a very difficult job," Roos said.
"They're a two-win team and 56 per cent - I think they're a better team than that.
"We need to get competitive - 56 per cent is an unacceptable percentage.
"My goal is to make them as competitive as we possibly can, as quickly as we possible can."
Roos said one of his first priorities was to keep out-of-contract duo Colin Sylvia and Jack Watts at the club in 2014.
"I really want them to stay and I want them to be part of the football club, and hopefully they do.
"It's a real priority for me to get those two quality boys linked to the club."
Roos said he did not have an immediate target to become his senior assistant coach and anointed successor.