The 47-year-old, who was in charge of Dunfermline Athletic until the end of last season, replaced Darren Young after he and the club parted company.
The Fifers are currently bottom of League One and suffered a shock defeat by non-league Banks O’Dee in the Scottish Cup last weekend.
East Fife chairman Jim Stevenson commented: “I am delighted to Stevie has accepted our offer to return to the club as our new manager. We received a number of applications from high profile candidates but after speaking to Stevie yesterday we are confident we have selected the right person to take the club forward.”
Crawford, who moves on from a coaching role at Edinburgh City, added:” It has all happened very quickly and it was the first job that I found myself attracted to since leaving Dunfermline Athletic in May. I would like to thank Edinburgh City for giving me the opportunity to speak to East Fife.”