Cokanasiga, who has been named in England's 31-man training squad ahead of the match against the Barbarians on May 27 at Twickenham, will join Bath for the start of next season.
The winger says he's looking forward to the next stage of his career with Bath and believes he can develop his game at The Rec after coming through the youth ranks with Irish.
He said on the Bath Rugby website: "I'm genuinely excited to be joining Bath. It's tough to leave Irish having loved my time there, and I'd like to thank everyone involved with the club for the opportunities they have given me.
"However, I feel the environment at Bath is exactly what I need to grow and develop as a player both on and off the field and ultimately achieve my international ambitions. There is huge potential to achieve success, and I'm really looking forward spending my long-term future with the club."
Director of Rugby Todd Blackadder says Cokanasiga has great potential and has backed him to make a big impact moving forward.
He said: "We're delighted to bring in Joe for next season. He's an exciting prospect and at just 20 years-old, has his entire career in front of him. We know he will bring a lot to the environment moving forwards and we are all looking forward to helping him achieve his full potential.
"Joe brings power, pace and a huge physical presence to the wing position, which will be invaluable to us for many seasons."