The Holy See said in a brief statement that Lee was relieved of his functions under paragraph 2 of article 401 of the Code of Canon Law, which covers both serious offenses such as paedophilia and corruption, and resignations on health grounds.
The Irish bishop publicly apologised in 2010 after admitting that his response to child abuse allegations in the mid-1990s was "seriously inadequate".
Faced with multiple claims of abuse by a priest in his diocese, Lee transferred him to another ministry, and waited two years before notifying the police, according to reports at the time.
In his statement on Tuesday, Lee said failing health was his sole reason for leaving.
"As you are aware in July 2011 I was diagnosed with serious illness and, since diagnosis, I have been under medical care," he said.
"Recently the medical advice to me has been that, in the interests of my health, I should retire from the office of Bishop of Waterford and Lismore," he added.
"Accordingly, I have in the past few weeks submitted my letter of resignation as Bishop of Waterford and Lismore to Pope Francis. The Holy Father has considered my request and graciously accepted my resignation."
Ireland, a predominantly Catholic country, has been rocked by a string of official reports on child sex abuse stretching back decades, and on Church leaders' complicity in covering it up.