Nielsen, who masterminded the Danes’ hugely unexpected UEFA EURO 1992 conquest, had been ill since undergoing a brain tumour operation last year and passed away, aged 76, on Thursday.
In a letter to Allan Hansen, the President of the Denmark FA, the FIFA President wrote:
"I would like to express my condolences on hearing that Richard Møller Nielsen has passed away.
"On behalf of the members of the international football community, I should be grateful if you could extend our deepest condolences to his family, friends and loved ones."
The former defender starred for Danish side Odense, and won two international caps, before his playing career was cut short because of injury.
Nielsen went on to coach the Danish U-21s before assuming the senior side’s reins in 1990. After qualifying for the next European finals because of Yugoslavia’s disqualification, Nielsen led the likes of Peter Schmeichel, Lars Olsen, John Jensen, Brian Laudrup and Kim Vilfort to a 2-0 win over Germany in the final in Gothenburg.
He went on to coach Finland and Israel, retiring after a spell at Kolding in his homeland.