Starting next month, Grade will become non-executive chairman of the loss-making group, which was founded by three former Goldman Sachs bankers four years ago.
According to the paper, Grade is stepping down as chairman of financial information provider Hemscott, while Ocado chief executive Tim Steiner said his "media savvy" would help the retailer communicate with its customers.
The move comes as speculation mounts over a possible IPO by Ocado, which delivers food from supermarket Waitrose. It operates in a fast growing market but one that is dominated by Tesco, Asda and Sainsburys.
According to the Independent on Sunday, the group recorded a rise in gross turnover to £152m in the year to November 2005, up from £90m in 2004, while losses widened from £41m to £45m. Debt also rose from £82m to £95m.
Earlier this month, the FT quoted the chairman of John Lewis, Ocado’s biggest shareholder, as saying the listing would not happen until 2008. "(A float in) 2007 is unlikely as Ocado has to have a good profit record rather than just a few months of profit," Stuart Hampson said. "Ocado is still loss-making and it is looking for volumes so the next six months are going to be critical for building that.”
The retailer raised £60m from its existing shareholders in March – a move which valued the group at about £500m.