Both Forest and Pompey are yet to make an official announcement but the details of the agreement, which will include a compensation package for Pompey, are believed to have been ironed out.
Cotterill will now head to the City Ground to put pen to paper.
"It's been finalised this morning but I can't sign any papers from down here," Cotterill told Sky Sports News.
"I've had a great relationship with everybody at Portsmouth and it's been quite upsetting. It hasn't been an easy decision and the players and staff have been nothing short of fantastic. It's been tough today."
He added: "Forest are a fantastic club. From the time that I knew about their interest it was obviously flattering."
Cotterill succeeds Steve McClaren who resigned 12 days ago after just three-and-a-half months in charge.
The 47-year-old led city rivals Notts County to promotion from League Two in May 2010 during a brief stint in charge at Meadow Lane before taking the reins at Pompey a month later.
He guided the south-coast club to a 16th-placed finish in the second tier last season despite their tough financial predicament and threadbare squad
Cotterill's appointment completes a remarkable two-week turnaround at the City Ground and is the first act of new chairman Frank Clark, himself only appointed on Wednesday after Nigel Doughty took the decision to stand down at the same time as McClaren, albeit remaining as owner.
Add to that the decision of David Pleat to depart his part-time consultancy role with Forest in late September and the Reds will be more than happy to get back to footballing matters this weekend and a trip to midlands rivals Coventry.