Abell, currently deputy director, will replace outgoing director Tim Toulmin, who announced in September that he would step down.
Abell was selected from a shortlist of four candidates, but PCC chairman Baroness Peta Buscombe said in a release that it was a unanimous decision to appoint Abell.
"Stephen has the breadth of experience and ideas for the future to make him the right person to succeed Tim Toulmin as director of the PCC. I am very pleased that he has agreed to take on the position, and look forward to continue working with him," she said.
Abell will take up the new post from December 19.
In August it was announced that the PCC would undergo a review of its operations by an independent group, led by outgoing PCC board member Vivien Hepworth.
The review will try to find out how the transparency of the commission's operations can be enhanced and whether the independent systems of accountability can be improved.
The commission recently received a record number of complaints following Jan Moir's Mail Online column on the death of singer Stephen Gately.
The number of complaints sparked discussion about the PCC's handling of third-party complaints.
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