King resigned on Friday following the Blues' failure to convince the supporter-led body to sell them back the freehold of Stamford Bridge, which they handed to CPO in the 1990s to prevent property developers making the club homeless.
Frankham, who was one of CPO's original directors, will act as chairman until December's annual general meeting, when he and fellow board members Rick Glanville and Bob Sewell will be up for re-election.
A statement released on the CPO website on Monday said: "Following the resignation of Richard King as chairman and a director of Chelsea Pitch Owners Plc, the remaining directors of the company have invited Steve Frankham to rejoin the board of directors and to act as chairman. He has accepted that invitation.
"Steve Frankham is a long-time Chelsea supporter, who was an original director when CPO was founded in 1993.
"He became its chairman in 1997 - when Tony Banks resigned as chairman upon entering government - and led CPO during its most successful period of fundraising.
"Upon his appointment, Mr Frankham said he relished the opportunity to lead CPO in this vital period and to help it achieve its historic objectives.
"Mr Frankham, together with the other directors of CPO, will be up for re-election at the forthcoming annual general meeting.
"The board would like to express its sincere thanks to Richard King for the huge contribution he has made to CPO over the last eight years."
Chelsea must decide whether to return with a revised - or even an identical - offer for the Stamford Bridge freehold before the CPO AGM. They failed to obtain the necessary 75% of the vote at Thursday's stormy extraordinary general meeting but their 61.6% could be enough at an AGM, where only 50% support is usually required for resolutions to be passed.
Source: PA
Source: PA