The Netherlands defender was linked with an exit from the Amsterdam Arena throughout the off-season, and a deal taking him to the French capital appears to be all but official.
The Dutchman is set to round off a summer of heavy spending for the Qatar Investment Authority-owned club, with the likes of Zlatan Ibrahimovic, Ezequiel Lavezzi and Thiago Silva having already joined PSG.
"Van der Wiel's signature shouldn't take too long," Ancelotti said.
"Christophe (Jallet) was our only player who could play on the right side of defence. He'll have to compete with Van der Wiel now, but I do not see that as a problem."
Ajax are reported to have received a sum of five million euros for the full-back, whose contract was set to expire at the end of the season.
Ancelotti's charges face Lille on Saturday as they look to end a run of three straight draws in Ligue 1.