Ferguson only informed his coaching staff of his decision to retire at the training ground on Wednesday morning - shortly before the official announcement was made.
Sky Sports News spoke to the Dutch coach outside Carrington and asked him when he heard the news.
"Just this morning, he called us into his office and said what decision he took," he revealed.
"It has always been on the cards, there is speculation every season and the manager kept his cards close to his chest - I think he felt the time is right now and he has made the decision."
Meulensteen believes that Ferguson has not taken the decision lightly and will have thought about his decision.
"He obviously is a man that thinks things through very well," he said.
"I am sure he has taken a lot of thought about making the decision and I wish him well, he has been absolutely fantastic for this club, for Manchester United, and I hope all the fans will give whoever comes in all the support he has got."
The former Brondby coach, who has helped Ferguson to four titles, admits this season's title-winning campaign was a big one.
"I think we have responded really well to big disappointment from last year and there was determination around the whole place and especially around the manager and I think he was delighted to win the title the way we did," he said.
Asked about how Sir Alex was feeling, he concluded: "I think a combination of relief in some ways."