The group's Funeralcare business has agreed to display a full range of prices online and at its funeral homes, one of the aims of the Fair Funerals campaign.
Richard Lancaster, managing director for Co-op Funeralcare, said: "Funeral poverty is a growing issue and it is absolutely key that we take action and play our part in helping to tackle this. The measures we have announced today are a further step on this journey.
"Being the first business to sign Fair Funerals' new enhanced pledge highlights our long-term intentions in wanting to ensure that against an industry backdrop of rising funeral costs, quality funerals remain both an accessible and affordable option."
Heather Kennedy, campaign manager for Fair Funerals, said: "When we're grieving, talking about money is often the last thing we want to do, and calling around different funeral directors to compare costs can seem very daunting. So it's absolutely essential that funeral directors put prices on their websites. Unfortunately most funeral directors don't do this."