The former England skipper has spent the second half of the season playing under Ancelotti at the San Siro and revealed the Milan players are ''pleading'' with their boss not to leave.
Beckham told The Sun: ''Carlo Ancelotti's man-management skills are exceptional. He is a brilliant coach.
''To have played under a manager of his quality is a real privilege. He is one of the greats. I have been lucky in my career to play under a few of the best in the business and he comes into that category.
''I just wish I had been able to play for him for many more years. It has been a lot of fun. Every single one of the Milan players adores him and doesn't want him to go. They are pleading with him to stay.
''I know wherever he goes, and whatever he does, he will always have my admiration and respect.''
Beckham insists Ancelotti can also be fiery as well as friendly.
''He is a low-key, private type of person. But there is another side to him. While I have never had the 'hairdryer' type treatment, I have seen it from him,'' said the former Manchester United winger. ''When he wants to get his point across, he does it in no uncertain terms!''
Meanwhile, former AC Milan coach Arrigo Sacchi hopes the club can hold on to Ancelotti this summer.
''I have not spoken to him, but I think we are close to a goodbye,'' Sacchi told Radio Kiss Kiss.
''Perhaps Ancelotti's experience at AC Milan is about to end but I repeat, I am not certain and I hope Milan are able to keep him.''