The 25-year-old made 73 appearances for the Bundesliga giants across two seasons before joining Man United last month in a deal which could rise to around £43m with add-ons.
Prior to De Ligt's move to Old Trafford, Bayern supporters expressed their displeasure of the rumours of his potential sale by starting up a petition to try and retain the services of the Netherlands international.
The Bayern supporters' petition made it clear they did not want to see De Ligt to leave the Allianz Arena, but Bayern were prepared to let the defender depart despite him having three years remaining on his contract.
A statement read: "We all want Matthijs de Ligt to stay at FC Bayern Munich. He has proven that he's a world-class defender, probably the best in our squad.
"Selling Matthijs de Ligt would be an absolutely horrible decision and we would definitely regret it. That's why we use our voice to call attention that we will NOT make this mistake."
Eberl: 'We feel more comfortable with Upamecano and Kim'
However, Bayern chief Eberl has since tried to calm fans over the transfer by explaining that the German club believe centre-back duo Kim Min-jae and Dayot Upamecano are better defensive options.
Speaking at a press conference as quoted by the Evening Standard, Eberl said: "I followed it, including the petition. I know that many fans identify with him.
"Nevertheless, I had to make this decision because we also had to sell players. We felt more comfortable with Upamecano and Kim because they can defend higher up the pitch. And then an offer came in for De Ligt."
As well as Upamecano and Kim, Bayern's new head coach Vincent Kompany also has Eric Dier, Tarek Buchmann and Hiroki Ito at his disposal, although the latter is currently sidelined with a metatarsal fracture.
De Ligt, meanwhile, has played in each of Man United's first four Premier League games this term and scored his first goal for the club in a 3-0 win over Southampton last weekend, before coming off in the closing stages with cramp.
Playing down any injury fears, De Ligt told reporters after the match: "I'm fine I just had a little bit of cramp the last five minutes. It's the first time I think in five months that I played three times in a row. I wanted to play until the end but the coach said it would be better to take me off."
It remains to be seen whether Erik ten Hag intends to name De Ligt in his matchday squad for Man United's EFL Cup third-round clash with League One outfit Barnsley on Tuesday night.