Ferdinand enjoyed a six-year spell as a player at the club and returned in a coaching capacity in 2008, while Ramsey was initially appointed to work with Tottenham's academy in 2004.
The duo had worked with the first team under previous head coach Tim Sherwood, who himself made the step up internally to replace Andre Villas-Boas at White Hart Lane last December.
However, Sherwood departed at the end of last season and Mauricio Pochettino was subsequently handed the reins last month.
The Argentinian has brought assistant manager Jesus Perez and first-team coach Miguel D'Agostino to north London, the duo having worked for him at previous club Southampton.
It has now been decided that Ferdinand and Ramsey will exit the club ahead of the new campaign.
A statement on Tottenham's official website read: "We should like to thank them for their contribution and wish them well for the future."
