Barker has been favourite throughout the process having worked with Pompey chief executive Mark Catlin before at Bury.
After interviews with all of Portsmouth’s seven-man shortlist concluded on Thursday, the club’s board met to vote on their preferred candidate that night.
And it has emerged that former Crawley manager Barker was the choice to replace Guy Whittingham.
Barker is set be joined by Steve Coppell in a director of football role, although it is believed Coppell will not be paid a wage.
Wilder was interviewed for the job, along with Exeter manager Paul Tisdale, caretaker boss Andy Awford as well as Steve Claridge and David Connolly.
Catlin, who previously helped appoint Barker at Bury, did not have a vote in the process as he is not on the Blues board.
Portsmouth hope to conclude contract negotiations with Barker over the weekend and appoint him as manager by Monday at the latest.