The 23-year-old will move to the Arms Park at the end of this season.
Blues rugby director Phil Davies said: "We are very lucky that we have got some very good scrum-halves here in Lloyd Williams, Lewis Jones and young Tomos Williams coming though, but we need depth and Tavis is a little bit different. As a unit, they will complement each other.
"Tavis is someone I've known from my Wales Under-20 days, where I gave him his cap, and he is a very hard working scrum-half.
"It's a terrific opportunity for us, and it's great for Tavis. I know he is delighted to be coming home, and we are delighted to have him."
Knoyle has been capped 11 times by Wales.