Davies made a sensational return to the City Ground on Thursday, almost 20 months after he was sacked by the old regime, replacing fellow Scot Alex McLeish as manager after the former Birmingham and Aston Villa boss' brief spell in charge ended on Tuesday.
After steering Forest away from relegation following his appointment in January 2009 and then masterminding successive Championship play-off campaigns during his first spell, Davies is on record as stating that he has "unfinished business" at the club.
Al-Hasawi agrees and is confident that, at the third time of asking following his family's takeover in the summer, he has appointed the right man to deliver top-flight football to the banks of the River Trent.
"I'm delighted to welcome Billy back to our club and really look forward to working closely with him," said Al-Hasawi.
"Billy has unfinished business with the Reds and we know how hungry he is for success. In returning to the City Ground we believe his leadership will help us fulfil our ambition of making it to the Premier League.
"Billy is a Forest legend who needs no introduction to our loyal fans. We know how excited he is to pick up where he left off last time and we will back him 110%. This is a very exciting appointment for us."
Davies remains popular among Forest fans and the Al-Hasawi family, the club's Kuwaiti owners, are keen to win over supporters following the turbulent start to their tenure.
The Al-Hasawis have made their third managerial appointment since completing their takeover after sacking Steve Cotterill and Sean O'Driscoll and seeing McLeish quit after just 40 days amid rumours of interference in team affairs from the owners.
The chairman added: "We know the fans, players and staff will join us in welcoming Billy back to the Forest family. As I have said, we will return Nottingham Forest to its former glory."