The Black and Whites have followed up the capture of England back rower Gareth Ellis by snaring the 20-year-old England Knights player, who rejected a new contract offer from the Tigers.
"We believe we're bringing in an extremely talented player with all the attributes to be one of the best centres in the competition," said Hull coach Peter Gentle.
"He is quick and strong and has an eye for the tryline, whilst he is another character that will fit in very well in the culture and environment we're trying to create here. I'd like to go on record and thank Castleford for allowing us permission to talk to Joe."
Arundel, who is currently sidelined with a shoulder injury, has scored 16 tries in 44 senior appearances since making his debut for Castleford as a 16-year-old in 2008.
"I'm looking forward to a new challenge and something a bit different," he said. "I'm really excited and also a little nervous as it's a big club and that will put a bit more pressure on me.
"But joining a big-city club with the rivalry they have with Hull KR and where the fans love the sport is something that really appeals to me. I will always be a Cas fan at heart. It's my home-town team and I love the fans there but I'm looking forward to a new challenge now."
Castleford are thought to have lined up two centre replacements in Hull KR's Jake Webster and St Helens' England international Michael Shenton, who left the Probiz Coliseum 18 months ago.
"While it is disappointing that Joe will no longer be playing for us next season, we did table an offer we felt represented his value which was rejected," said Tigers chief executive Richard Wright.
"We have been outbid on this occasion by a club with much bigger resources at present and we are not in a position to over pay. Joe will, however, leave the club at the end of the season with nothing less than our best wishes for the future."