The former England lock led the Exiles to promotion to the Aviva Premiership last season but they look set for an immediate return to the Championship after 15 defeats from 17 games.
Kennedy was given the chance to remain in his position and work alongside new technical consultant Declan Kidney and head coach Les Kiss, but the 35-year-old requested to leave the club and they “reluctantly accepted his resignation”.
“Nick will always be a major figure in the London Irish history books,” said Mick Crossan, London Irish’s president and majority shareholder.
“He was an excellent player and we believed that he had a promising career in front of him as a coach, which we had hoped that he would fulfil under the guidance of Declan Kidney and Les Kiss. So, we’re disappointed that he has decided to move on.
“However, we have accepted his decision and wish him all the best for the future.”
Kennedy made over 200 appearances for Irish in a decade-long playing career and was part of the side that reached the Premiership final in 2009.
“London Irish will always have a special place in my heart,” said Kennedy. “This was not a decision that I made lightly as there are a great bunch of coaches and players at Hazelwood.
“I’m proud I helped change the Academy from a two star to a five star RFU rating and to have gone undefeated for a season to win the U18 Premiership Rugby title.
“I’m proud we won the Championship at the first time of asking, only losing one game all season, and I’m very proud of the players and how they fought to the end of every game.
“I’d also like to thank the fans for their outstanding support over the years, and I hope that they will be enjoying success in the future.”