Jones' new contract has a performance-based break clause based on England's showing at the 2019 Rugby World Cup.
There had always been an inkling that Jones himself might fancy a little more time at the sharp end.
England open their campaign on February 4 in Italy and ahead of the Red Roses' three in a row bid, Jones has signed a deal that will keep him in charge at Twickenham until 2021.
"I did not presume I would be asked to stay on but, once the conversations started very recently, it was not a hard decision to make", Jones said.
"This is likely to involve appointing a new head coach by the end of the 2019/2020 season, with a view to a smooth coaching transition", it said.
The Red Rose won the Six Nations a year ago after winning four of their five games, but suffered Jones' sole defeat of his England tenure in the final game in Ireland.
"These are exciting times for English rugby, with a focused and committed squad who are full of potential and determined to win", said Jones. The new coach would then lead England into the 2023 Rugby World Cup.
'Under Eddie's leadership, we have risen from eighth to second in the world - and Eddie won't be satisfied until we are number one.
"He has a 95 per cent win rate at the helm, and has been a galvanizing force for the RFU, bringing focus, clarity and extraordinary commitment to the role".
"We now have a robust succession planning process in place which will avoid the historically disruptive pattern of resetting the coaching team and performance system every four years. Eddie will be a big part of this process, and wants to ensure a smooth handover to his successor".
Jones is set to name his squad on Thursday ahead of England's opening Six Nations match against Italy on February 4.