Sullivan scored over 250 tries in 352 appearances for FC before crossing the river to KR, where he added a further 118 tries in 213 matches.
He also represented GB and Wales, as well as serving a spell in the armed forces, before being awarded the MBE. He died in 1985, aged 42.
The Clive Sullivan Trophy was first awarded in 2001, but now in its more formal setting at the beginning of every season, both club owners feel it is the most fitting way to celebrate one of their most iconic heroes.
FC's Adam Pearson said: "When you think of Hull FC and Hull KR, you immediately think of Clive Sullivan.
"The Trophy has been around for a number of years, but with both clubs playing each other more regularly in pre-season we felt it would be more appropriate to formalise the trophy and play an annual fixture that carries his name, ensuring his legacy and contribution to the game is never forgotten."
Hull KR CEO Mike Smith added: "For Clive to be held in such esteem by fans of both clubs says it all.
"The annual friendly is always a great occasion and in what will be the 35th anniversary of Clive picking up the Challenge Cup at Wembley in the red and white of Hull KR, the naming of this game is a fitting tribute to a true legend."
Tickets are now on sale for the game at the KC on January 18.
