"I think this is the biggest and best news for all of us," Eberl told ARD.
The sporting director explained the exact circumstances behind the coach's absence for the first time: "They found out what it is: meningeal irritation caused the incident last Friday."
Kompany collapsed on the sidelines of the second Bayern team's training session last week, and a viral infection had previously been mentioned - a virus is often the underlying cause of meningeal irritation.
"But he has now been allowed to go home and can complete his rehabilitation there," Eberl said. "For him, rehabilitation means rest and medication. And then I am very, very sure that he will soon be back on the touchline at 100 per cent.
The director added that the club won't rush to get Kompany back on the touchline: "(He will be given) all the time he needs - we have always said that. That is why we spoke of weeks from the very beginning."