The Manchester United boss described his fellow Scot as a "fantastic man" and "great friend."
Few contemporaries could come close to matching the longevity of the award-winning football writer, who covered no fewer than 14 World Cups in his career.
Sir Alex said he knew Brodie for 40 years. "He's nothing but a great friend and always good value in terms of opinion," he said. "He cut to the chase, quite simply that's who he was - straight talking."
Among his accolades, Brodie was awarded an MBE and an honorary doctorate by the University of Ulster.
Fifa also recognised his contribution to journalism, presenting him with his own miniature version of the World Cup trophy to mark the number of tournaments he had attended.
Fifa vice president Jim Boyce said he would miss him dearly. "He was the doyen of Northern Ireland football, a very, very trusted journalist and his main aim in life was to promote football," said Belfast man Boyce.
Fifa president Sepp Blatter paid his own tribute to Brodie, someone he described as a "gentleman". "I can tell you that Malcolm Brodie, also an MBE, he was appreciated in the world of the international media," he said. "When he was in the media centre in the World Cup he was appreciated, he was respected, the colleagues they went to him and said 'Hello Malcolm, how are you?' and whatever. He was a legend there in."
Mr Blatter said he had been speaking with Brodie as recently as last month. "He was very highly appreciated on the international level," he told BBC Radio Ulster. "I remember I was just starting in Fifa at the first World Cup in 1978 when I personally attended in the officiality of Fifa, in 82 and 86 and everywhere - Malcolm was there. When he was not any longer there we were missing him and we are going to miss him."