The 18-year-old full-back, born in Bangor and who began playing rugby at Caernarfon RFC, shone during the tournament and was a key part of Jason Strange's side.
"I'm very happy to have signed for Cardiff Blues," he said.
"It's a big opportunity for me to continue to develop as a player in a professional and elite environment, which is what I've come through in RGC with both their facilities and their pathway.
"I'm looking forward to the future and what it holds for me.
"You only need to look at some of the players in the senior ranks at Cardiff Blues who I can look to as an inspiration."
Wales fought their way to wins over Ireland, Scotland and France in the opening rounds before more convincing wins over England Italy sealed the title for Williams and his teammates.
The man from north Wales will join up with Blues' elite performance pathway manager Richard Hodges with the end goal of forcing his way into Danny Wilson's first XV.
Rhys Patchell, the highest scorer in the Guinness PRO12 this season, is the man currently in possession of the Blues 15 shirt and has scored six tries this season but is set to join the Scarlets in the summer.
Williams progressed his career with renowned development team RGC 1404 and Hodges is keen to maintain the Blues' strong relationship with them.
He said: "We are very happy that Rhun has signed for us from the 2016/17 season onwards.
"We have a strong relationship with RGC and have seen players like Joe Jones come through that system and now Rhun, he is an outstanding prospect."
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