He replaces David Burke who left to join global ground engineering contractor Keller in October.
Ledwidge was finance director at Morgan Sindall Construction & Infrastructure for eight years, and before that worked at Carillion Construction for 12 years.
A Murphy spokesman said: “We are pleased to have Joe on board – he brings a wealth of experience to Murphy and we believe he is the right person to take our approach to disciplined financial management forward.”
He added that Ledwidge “would support its new company strategy called Murphy at 75.”