Neuer has not played a competitive match since September after suffering a recurrence of a foot injury, but the 32-year-old has come through training unscathed this week.
The goalkeeper's progress has led to Heynckes declaring Neuer available for the World Cup, and he has backed the stopper to play an influential role for the defending champions.
At a press conference, Heynckes told reporters: "He's completed full training every day since Tuesday. It's really good news - he's absolutely pain free and in physically very good condition after working so hard and in exemplary fashion for months in the gym.
"He will be back and integrated soon - he has too much quality and talent. He has a presence and authority in goal which is incomparable. The national team can breathe a sigh of relief - he will not only be fit, but he will also be a big factor for the German team."
Neuer will remain out of the starting lineup for this weekend's DFB-Pokal final with Einchtart Frankfurt.