Ostrom, who resigned from 118 118 in March, described his new role as "an amazing career opportunity".
The move reunites him with former 118 118 chief executive Chris Moss, who joined B&Q as its customer and marketing director last October. Ostrom said he had known Moss since the mid-nineties when the pair worked for rival telecoms companies Cellnet and Orange.
Ostrom said: "What Chris did with Orange was really a transformational campaign at a time when the market leader [Vodafone] was firmly mired in the thinking that this was a device for business people.
"If you look at Chris's work for Orange, Virgin Atlantic and 118 118, one thing he has always done is pull off memorable campaigns; I understand his approach to marketing very well and I've a pretty good idea of how PR fits into that agenda."
He added that he had been "knocked back by the integrity of the brand" since joining three weeks ago.
"Just on wood products, 99.8% is sustainable and the remaining 0.2% is sandpaper for power tools. B&Q has an incredible lead in terms of its corporate citizenship and part of my role with the business is to uncover all those good things that are going on and communicate them to the customer," he said.
He added: "The job is emphatically not about trying to amplify small points of difference, but simply getting B&Q and its brand the scale of recognition for what it already achieves for its customers and all the good things to come as one of the UK's top retail businesses."
Ostrom's appointment follows B&Q's decision to switch its press office and PR campaign work to Good Relations after four years with Z PR and its advertising to WCRS without a pitch after parting company with Karmarama.
Commenting on B&Qs latest advertising campaign, Ostrom said: "It very much makes the customer the hero and the brand takes a secondary role facilitating what the customer wants to do. B&Q has a fantastic array of products, but the way to make that resonate is to show what that means to the customer in their everyday life."