Reporting to John O'Keeffe, BBH's executive creative director, Tesch will work across a range of digital clients and on above-the-line business.
He joins from Lowe Tesch in Sweden, where he was the co-founder, creative director and chief executive.
Tesch is the second digital creative director hired by the agency in the space of a month as it looks to extend its digital capabilities. Dominic Goldman joined as a digital creative director in October.
Tesch said: "What really got me interested was that BBH seemed very serious about the digital conversion of the agency. It was also very keen to get me in the centre of things."
During his career, Tesch has picked up a number of awards, including gold Lions at Cannes in 2004 and 2005 for his work on Saab and 3.
In 1996, he launched Tesch & Tesch, one of the first digital agencies in Scandinavia. It was then bought by Lowe Worldwide and became the digital offering for Lowe Brindfors in 2006.