The Pompey boss is on the brink of departing Fratton Park – 23 days after winning the League Two title.
Compensation has been agreed with the Latics, with 12 months remaining on his existing agreement, and the 50-year-old will now end his south coast stay two years on from joining from Chesterfield.
Cook is likely to take assistant manager Leam Richardson and the rest of his existing coaching staff with him to the DW Stadium.
It represents a speedy closure to a dramatic few days after the newly-relegated Championship club made their move on Friday.
The Liverpudlian was handed an improved contract and bonuses after securing promotion for the Blues, as written in his existing deal.
There was another written offer made over the weekend in light of Wigan’s bid to secure his services.
It still fell short of what Latics chairman David Sharpe had tabled after meeting Cook in Spain at the weekend.
With Pompey not prepared to overstretch themselves as they wait for Michael Eisner’s takeover to be completed, that paved the way for his exit.
Cook had stressed he was keen to remain at Fratton Park in the wake of winning the title, and has continued to privately repeat that stance in recent days.
There was some concern about the safety of his position moving forward under Eisner’s Tornante company, however. He has also shown frustration at the existing £3m playing budget he’s working to and missing out on summer targets in recent weeks.
The former Wigan player’s standing is also on a high after being named the League Manager’s Association League Two manager of the year last week.
The Blues feel they’d gone as far as they could, however, and will now turn their attention to finding their fifth manager of the community era.
Cook is expected to be given a significant playing budget at his new club in addition to a lucrative deal.
The move also means a return to Fratton Park next season in the away dugout, with Wigan and Pompey due to meet in League One.
Cook departs the Blues with one of the most impressive win ratios of any of their managers.
He delivered 52 victories, 28 draws and 27 losses from his 107 games in charge – and ended this term with a flying run of 10 wins and a draw from 12 matches to secure the championship with a 6-1 final-day win over Cheltenham.