Reed, the associate creative director of Tribal, replaces Jon Williams, who joined Grey at the start of the year.
Reed is completing his notice period at Tribal and will start at BMB in August. He will report to Trevor Beattie, the agency's creative partner, and lead the agency's digital output on clients including Carling, ING Direct, Pretty Polly and Thomson.
Reed, a former creative partner of Tribal's creative director, Ben Clapp, has been at Tribal for seven years.
He was most recently the associate creative director of the agency, winning a number of awards for his work on The Guardian, Johnson & Johnson and Volkswagen.
Andrew McGuinness, a partner at BMB, said: "Stephen is a great find as he is a terrific digital evangelist, yet has proven experience of working alongside senior creatives. We're thrilled that he's joining what has become a mighty strong team."
Reed added: "The lure of an agency with the talent and dynamism of BMB, led by Trevor, Andrew, David (Bain) and Bil (Bungay), is an opportunity not to be missed."
The appointment comes three months after BMB poached Alison Lomax from Agency Republic as its digital client services director. In January 2007, BMB hired Jon Williams and Nick Stewart, the joint managing partners of Harrison Troughton Wunderman Interactive, to head its digital offering. Williams, who before HTW was the interactive chief at Publicis, left a year later to join Grey, replacing Dave Alberts as its top creative.