The pair have reached an agreement with the RFU after losing their roles with the national team in the wake of England's quarter-final exit at the World Cup.
Earlier this month, Stuart Lancaster was selected to head up a new-look interim England coaching team for the Six Nations campaign which also includes Graham Rowntree and Andy Farrell.
Ford and Wells had respectively taken charge of England's defence and forward play since 2006, coaching the team on two World Cup campaigns.
Acting RFU chief executive Stephen Brown said: "John and Mike have given great service to England and rugby in this country over many years and their contribution is appreciated.
"As well as his role with the senior team, John has played a major part in developing players as a national academy coach since he joined the RFU in 2005.
"In his five-and-a-half years with the senior team Mike created one of the best defences in world rugby, and while the World Cup was obviously disappointing overall, it should be noted that England conceded just three tries in their five matches - the joint lowest in the tournament.
"On behalf of the RFU I would like to wish them well in the next stages of their careers."
Ford and Wells coached England to the 2007 World Cup final and they leave at the end of a rollercoaster year.
England began 2011 in positive fashion, having beaten Australia home and away in 2010, and went on to win the RBS 6 Nations title.
But the year finished in disappointment at the World Cup, which led to team manager Martin Johnson and attack coach Brian Smith standing down.
It became clear when Lancaster's interim was announced that Ford, who coached with the 2005 Lions, and ex-Leicester boss Wells had also reached the end of the road with England.
Ford said: "To be England's defence coach over the last five and a half years has been an absolute honour and I have worked with some great players and management.
"The World Cup was a watershed and it is time for a new environment. I wish Stuart and everyone the very best for the Six Nations and I firmly believe that England can win it."
Wells will always look back on the 2007 World Cup quarter-final victory over Australia and the semi-final triumph against France as the highlights of his tenure.
"It has been a real privilege and a great honour to have been involved with the RFU for the last six years," Wells said.
"I have been part of a very successful national academy and England Saxons set up and been to two World Cups including a World Cup final in 2007, with the victories over Australia in Marseille and France in Paris as stunning highlights with the England team.
"Now is the right time to move on to look for a new challenge within the game.
"I am proud to be leaving at the end of a year in which England has introduced a wealth of young talent, won 10 out of 13 games and are the current Six Nations champions."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.