The midfielder completed a deadline day switch to Colchester on a two-year deal after spending the summer seeking a new club.
Having offered the 22-year-old former West Ham and Charlton player a three-year deal in December, the Blues were entitled to receive compensation.
Rather than taking the issue to a tribunal, a settlement was reached with the League Two strugglers, although Cullen declined to reveal the precise amount involved.
Regardless, it finally ends the long-running affair.
The Blues chief executive told The News: ‘We got to the stage over the summer where it was quite clear Jay had no intention of signing for Pompey, so we removed the contract offer.
‘However, we had to continue paying him beyond his severance on the basis that if we stopped then we’d lose our compensation rights.
‘I am pleased Jay has finally found a club and we haven't had to go to a tribunal. We’ve been able to reach a compensation agreement with Colchester and, ultimately, it has worked out okay for both parties, given our decision to withdraw the offer.
‘It’s not necessarily a large sum of money, but we had to be mindful of compensation if we went to a tribunal.
‘One of the key factors is looking at the length of time the player has been at the football club. Jay is not Academy-developed here, but a player who has been with us for two years.
‘You always get a degree of uncertainty about a tribunal. Having looked at a couple of these over the years, I’m always of the mindset that it’s best to try to get a compensation agreement for whichever party.
‘We have also made sure we’ve protected ourselves should Jay go on to have a really successful career and move on again, so there is something in it for Portsmouth Football Club.
‘But I am pleased for the player as well because he now has an opportunity to get back playing football – and we wish him well at Colchester.’
Mingi made 29 appearances, scoring once, after arriving at Fratton Park on a free transfer in September 2021.