His seven years in charge of Wakefield between 1987 and 1994 followed a 13-year playing career with the club.
He won the Lance Todd Trophy as Man of the Match in their last Cup final appearance in 1979.
Topliss was also in charge of the Great Britain Under-21 side in 1989.
Terry Crook, who played alongside Topliss more than 300 times for Wakefield, told BBC Radio Leeds: "I'm absolutely shocked and devastated.
"David was an absolute gentleman and he was very, very fit. He was lean and not overweight, and to hear news of somebody who meant so much to me as a player, and all the players who played with David, I'm in shock.
"Many is the day if down at Trinity we were struggling with a few minutes to go, it would be 'Come on Toppo, bit of the magic' and he'd turn it on and he'd win you the game.
"He was a tremendous player and a very likeable and knowledgeable person."
Rugby Football League chief executive Nigel Wood paid tribute to Topliss' "skill, bravery and sportsmanship".
He said: "As a player, David reached the very highest levels of the domestic and international game. He was admired by many in both northern and southern hemisphere rugby league.
"David was also very committed to making a continuing contribution to the game and was a regular at many matches.
"He was also a massive enthusiast for playing touch rugby league, which again illustrated his passion for the sport."
When you look back to the try he scored in the 1982 Challenge Cup final replay that set us on our way to victory, it was one of many significant moments that David played in the club's history
Former Hull team-mate Lee Crooksn
Lee Crooks, who played alongside Topliss when Hull won the Challenge Cup in 1982, told BBC Look North: "When you look back to the try he scored in the [final] replay that set us on our way to victory, it was one of many significant moments that David played in the club's history."
Hull chief executive James Rule, speaking as tickets went on sale for the Challenge Cup semi-final against Wakefield, said: "We'll certainly make our own tribute at the Warrington game and something around the semi and final if we are lucky enough to get there."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.