Current chairwoman Pam Duxbury announced the sale to the company she owns with Sage Investments Ltd.
Duxbury said a nominal payment was given to Coxall for the deal.
Coxall resigned as chairman in May, days before the club's relegation from the Football League, having taken over with JPNG in 2015.
Last season Pools faced three winding-up petitions before Coxall quit, saying it would "divide the club" if he was to continue in the role.
In the statement on the club's website, Duxbury said she had averted the club going into administration "several times" in recent months.
"The last six months have been the most difficult I have ever encountered in my professional career and I am very relieved to be on the other side," she said.
She also confirmed future plans for the club's ownership to be split between the club's Supporters' Trust and a consortium of individuals willing to invest.
National League side Hartlepool United have been taken over by HUFC Holdings Ltd, ending the tenure of former chairman Gary Coxall and owners JPNG.