The 32-year-old New Zealand-born second-rower played in the NRL for Parramatta Eels and had two seasons with Catalans Dragons before joining Giants in 2020.
Tigers will be hoping he can make a similar impact to Suaia Matagi and Jordan Turner who both joined them from Huddersfield ahead of the 2021 season.
Edwards will replace Oliver Holmes, who is heading to Warrington Wolves and Radford said: “I am so excited about working with Kenny, I’ve actually tried signing him on a couple of occasions, so to get to work with him now, I’m buzzing.
“I love the energy he brings on a matchday, - he always plays on the edge of right and wrong and has a fantastic skillset for a back-row player.
“I am sure Kenny will be a great addition to an already strong left-edge.”
Edwards, a member of the Combinated Nations side which beat England this year, described his move to Tigers as "amazing" and said he can't wait to get started.
"I spoke to Radders back earlier in the year and to finally get it done, I am over the moon," he said.
“I am good mates with Suaia Matagi and Jordan Turner who I was with at Huddersfield last year.
"I was speaking to Suaia because he started at Castleford in the pre-season and from the get-go said how professional it was.
"He loved the pre-season and I actually started to get a little jealous.
“The way he and Jordan have sort of turned their careers around while being there, JT has turned into one of the best wingers in the competition this year.
"The style of footy that Castleford plays, I really think it is going to suit me.”
Edwards also feels he will work well with Radford.
He said: “When I first left Australia and was heading this way, my good mate Bureta Faraimo - who was at Hull FC with Radders - gave me a call and said they were keen to get me.
"At the time I had my heart set on Catalans Dragons, but I have had a bit of history with Radders in the past.
“I have spoken to players who have played under Radders and I know the way he likes to coach.
"Speaking to Radders a little earlier on in the year and when he was pitching for me to come to Castleford, everything he said pretty much summed me up as a player.
"He has been able to win a couple of Challenge Cups with Hull FC and to be able to start working with him, I can’t wait.
“I wish I could start pre-season next week and when the season starts next year, hopefully, we can be all guns blazing.”
Edwards' Giants career came to a controversial enbd.
He served a 10-game suspension for inserting a finger into the backside of Catalans' Sam Kasiano during a game in July and was not selected by Giants after that.