The former East Fife boss, who has had two spells at Tynecastle previously during Jim Jefferies reign, has been working under Gary Locke on a short-term, voluntary basis.
The 62-year-old told the Hearts website: "I didn't enjoy being out of the game and came here with the intentions of helping Gary and the club as much as I could.
"I have a lot of enthusiasm for the club and the job and I'm very excited about what's happening here at the moment.
"We have the whole season to keep chipping away at the teams above us. The young players have done exceptionally well so far and they will only get better - but it is not going to be an easy task."
Locke said: "Billy knows everything there is to know about the Scottish game and to have someone of his enormous experience here is a boost."
Hearts, who began the season with a 15 point deduction having entered administration in June, have reduced the deficit to 11th-placed St Mirren to nine points after five games.