IRB Council Member for Wales Gerald Davies, a former Cardiff and Lions wing, presented the commemorative cap and gold pin to Cardiff Athletic President Dr Charles Derek Williams.
"I am honoured and delighted to be inducting two greats of the Game in Wales, a great club and a great player and captain who significantly contributed to the history and the playing of Rugby, not just in Wales but worldwide," said Davies.
They were handed the award under the theme 'creativity and ingenuity' for pioneering the three-quarters back-line that we see today.
The move came out of necessity, with injuries forcing Cardiff's selection committee to select Hancock as an extra centre at the expense of a ninth forward.
But Hancock played so well that they stuck to the formation. And the decision came with great success, with Cardiff winning all but one of their games during the 1885-86 season in which they scored a staggering 131 tries while conceding only four.
The system was adopted by Wales in the 1885 international season and soon spread worldwide.
"Cardiff and Hancock had a huge influence on the development of the game and how it evolved in the early days of the game," added Davies.
"Vision, creativity and innovation - those are all things important today."
Cardiff, in both their club and regional guises, have also had a major influence on the Lions.
They have contributed 45 players to Lions tours including greats like Gwyn Nicholls, Bleddyn Williams and Gareth Edwards.
During the 2009 tour to South Africa, Cardiff Blues were represented by five players, namely Gethin Jenkins, Andy Powell, Martyn Williams, Jamie Roberts and Leigh Halfpenny.
"They've made a substantial contribution to the Lions over the years," added Davies, the 2009 Lions tour manager.
"There's always a group of players from Cardiff going on the Lions tour. We had quite a clutch of them last time
around, and if you look back over the years, no Lions team has left these shores without a Cardiff representative."