The Church had joined with other shareholders for the "Aiming for A" coalition which urged BP to consider its climate change resolution: 'Strategic Resilience for 2035 and Beyond'.
It means the company will now recommend to other shareholders that they back the resolution at the next AGM.
Shell has accepted a similar proposal.
Edward Mason, Head of Responsible Investment for the Church Commissioners, said: "The positive way in which BP and Shell have responded to our shareholder resolutions is completely unprecedented.
"This represents a step change in engagement between institutional shareholders and the oil and gas industry on the strategic challenge that climate change poses to the industry.
"The next step is for investors to back the boards of both companies and to vote for the disclosures that we have requested and that the companies have said they will provide.
"We look forward to seeing the new in depth reporting from both companies later this year and to continued engagement".
BP and Shell have the biggest carbon footprints of all the companies listed on the London Stock Exchange.
The shareholder resolutions are intended to challenge the companies to run their businesses so that they participate constructively in the transition to a low carbon economy.
The resolutions also provide an opportunity to the shareholders of both companies to signal that they want to see BP and Shell adapt their businesses over the long term.
The resolutions will be voted upon by shareholders at the BP and Shell AGMS this spring.