Cokanasiga played an integral part in helping Irish get promoted to the Aviva Premiership last season, scoring five tries in 12 appearances, and there was said to be growing interest in him.
The 19-year-old is already making huge strides on the international after he helped England's Under-20's win the 2017 Six Nations before being included in the senior squad for the tour of Argentina over the summer.
The Exiles have managed to tie the wing down to a long-term stay at the Madejski Stadium and Kennedy is looking forward to watching the continued development of his rising star.
"Joe is a fantastic prospect for London Irish who leads the way with his work rate both on and off the pitch," he said. "We're delighted that Joe wants to be part of the London Irish's long-term future and his decision to re-sign is a massive boost for the club as we continue to create a pathway for our brightest talents."
Irish are currently sitting 11th in the Premiership, having won just one of their five matches to date, and they face a tricky challenge at home to Leicester Tigers, who are sixth in the table, on Saturday.