Cotterill revealed earlier on Friday that he had agreed to take the reins at the City Ground and that the details of the agreement, which are understood to include a package in the region of £250,000 for Pompey, had been ironed out.
The 47-year-old subsequently travelled to the east midlands on Friday afternoon and put pen to paper on a three-and-a-half-year deal.
Pompey confirmed the departure of Cotterill in a statement on Friday night.
It read: "Portsmouth can confirm that Steve Cotterill has parted company with the club to take up the manager's post at Nottingham Forest.
"A compensation agreement has been made with Nottingham Forest over Cotterill's departure to the City Ground.
"Portsmouth would like to thank Steve for his efforts during his 16 months at Fratton Park."
Forest have been seeking a new manager since Steve McClaren resigned 12 days ago after just three and a half months in charge.
The City Ground side are lying 21st in the Championship table - two places and one point below Portsmouth - and are due to play at Fratton Park on November 5.
Cotterill 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 subsequently guided the south-coast club to a 16th-placed finish in the second tier last season despite their tough financial predicament and threadbare squad.
Those credentials may well have enticed new Forest chairman Frank Clark, who was himself only appointed on Wednesday after Nigel Doughty took the decision to stand down at the same time as McClaren, albeit remaining as owner.
The appointment of Cotterill completes a remarkable two-week turnaround at the City Ground, especially when added to the decision of David Pleat to depart his part-time consultancy role with the club in late September.
The Reds will be more than happy to get back to footballing matters on Saturday and a trip to midlands rivals Coventry.
Cotterill is expected to be watching from the stands at the Ricoh Arena as existing assistant manager Rob Kelly takes charge, prior to an official unveiling on Monday.
Meanwhile, coaches Stuart Gray and Guy Whittingham will take charge of first team affairs for Portsmouth's home match against Barnsley on Saturday as the club seeks a new manager.