He announced a leave of absence in January after the incident was brought to light. He said on Tuesday that during his time off he "reflected" and has "come to see that many wrongs occurred in 1998."
Savage added: "The first was my inappropriate relationship with Jules, which was not only immoral, but meets the definition of abuse of power since I was her youth pastor; therefore, when our relationship became physical, there could be no claim of mutual consent.
"Another wrong was the failure to follow due process afterward; Jules deserved, and did not get, a full investigation and proper response 20 years ago."
He said that stepping down from his position came after much prayer and counsel.
"I know that stepping down... still doesn't make things right for Jules," he explained. "But addressing my own acts of abuse this way acknowledges the importance of confronting abuse in our culture and in the Church at large."
Following his resignation statement, Highpoint Church announced that an independent review into the incident had been completed and the investigation found no other instances of abuse in Savage's ministry.
The church said: "Highpoint leadership has come to recognise that it was defensive rather than empathetic in its initial reaction to Ms. Jules Woodson's communication concerning the abuse she experienced, and humbly commits to develop a deeper understanding of an appropriate, more compassionate response to victims of abuse."
The church has organised an assessment of its current training, policies, screening practices and supervision in ministries serving minors.
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