White passed away following a short illness - just two days after the death of former vice-chairman Jack Gillespie.
The current Rangers non-executive chairman Walter Smith revealed the news about White on Wednesday.
Smith said: "We are all saddened by the news of Davie's passing and our immediate thoughts are with his family.
"I remember when he was appointed as manager and he had such a difficult job at that time, not just because he was following Scot Symon, but because Celtic were enjoying the best period in their history under Jock Stein.
"Davie was also manager of Dundee when I was with Dundee United and, ironically, be brought the League Cup to Dens Park in 1973 by beating Celtic.
"He was a great Rangers man and scarcely missed a match at Ibrox."