Cooper followed his training session as Forest boss on Tuesday morning, with the league’s lowest club next in home action against Millwall on Saturday.
Forest will then travel to Barnsley on Wednesday 29 September – live on Air sports.
Cooper becomes Forest’s 14th permanent leadership position in the past 10 years.
Wednesday 29 September 7:40 p.m.
Nottingham Forest Managers – Last 10 Years (Matches in Charge)
Steve McClaren (13), Steve Cotterill (37), Sean O’Driscoll (26), Alex McLeish (7), Billy Davies (59), Stuart Pearce (32), Dougie Freedman (57), Philippe Montanier (30), Mark Warburton (37), Aitor Karanka (52), Martin O’Neill (19), Sabri Lamouchi (55), Chris Hughton (53)
(excluding interim managers)
Forest agreed to compensation with former Cooper club Swansea late last week as he was still technically under contract with the Welsh club.
He left Liberty Stadium as head coach in July after leading them to the Championship playoffs.
Cooper, who guided England to the U17 World Cup in 2017, was immediately identified as the preferred candidate after Chris Hughton was sacked.
“Steve was our first choice as a head coach and we are delighted to have secured his services. His record of developing young talent is exceptional, ”said Forest CEO Dane Murphy.
“Steve knows what it takes to be successful in the Championship and has proven himself with Swansea.
“We reduced the age of our team over the summer and Steve is the perfect coach to merge a team and start moving up the standings.
“On behalf of the owner and the board of directors, we welcome Steve to the club and look forward to providing him with all the support he needs to be successful at Nottingham Forest”.
Forest started the championship campaign with a draw and six losses.
Following Hughton’s departure, Coachless Forest earned his first league win of the season with a 2-0 victory at Huddersfield.
With interim head coach Steven Reid overseeing Saturday’s game, a first-half strike from Lewis Grabban and an own goal from Lee Nicholls just after half-time saw Forest collect all three points. .
It was also the first time they had scored more than one goal in a league game since April.