Viestad has a cand.mag. degree from the University of Oslo, As his academic background is studies in history, political science and media science, his stated culinary qualification is an all-consuming preoccupation with food, where research is as likely to be conducted in a library as a laboratory or a kitchen. He frequently emphasises that he is not a trained chef.

From 1995 to 1997, Viestad wrote for Morgenbladet, between 1997 to 1998 for Dagsavisen, and has been with by Dagbladet since 1998. His weekly column in the Dagbladet weekend supplement Magasinet titled "Det beste jeg vet" began in 1999, initiating his collaboration with the photographer Mette Randem of critical acclaim.

Viestad has been involved with the "molecular gastronomy" movement since 1999, working especially with French food scientist Hervé This at the Collège de France in Paris, and was a member of the International Workshop for Molecular Gastronomy, where he has participated with food scientists such as Harold McGee, and Peter Barham and chefs Heston Blumenthal and Pierre Gagnaire. In his popular Washington Post column he writes about the science of everyday cooking.

In 2003, Viestad premiered as the host of the public television series New Scandinavian Cooking. With 5 million U.S. viewers per episode and a global reach so vast it was at the time viewed as the greatest ever exposure of Norwegian culture, second only to the 1994 Lillehammer Olympics. As the host of seasons one, two, three, five and six, Viestad became internationally known. In 2008 the series included four hosts and was named Perfect Day, of which Viestad was a co-host. Viestad is the host of the fifth season of New Scandinavian Cooking, airing in 2010, and a sixth season is under production.

On a visit to Zanzibar, hotelier Emerson Skeens offered Viestad the position of "consultant chef" at the Emerson Spice Hotel, which Viestad accepted. Though an unpaid position, Viestad has said "One only gets to run a restaurant in Zanzibar once in a lifetime". His book Where Flavor Was Born: Recipes and Culinary Travels Along the Indian Ocean Spice Route (2007) was a departure from previous themes of Scandinavian cooking. The book was selected the "Best Foreign Cookbook in the World" at the Gourmand World Cookbook Awards in April 2008. His book on Norwegian food was awarded Special Price of the Jury at the 2009 Gourmand World Cookbook Awards.

Since February 2008, Viestad has written a monthly column titled "The Gastronomer" for The Washington Post about the science of everyday cooking. Viestad's recipes and writing have also been published in Gourmet, The Sunday Times, Vanity Fair, Food & Wine and Vogue.

Viestad has stated that he admires food writers Jeffrey Steingarten and Nigel Slater, chefs Alice Waters and Pierre Gagnaire, and Norwegian chefs Eyvind Hellstrøm and Bent Stiansen. The food writers of the great London newspapers are his role models, as they "operate in the grey zone between food columns and consumer journalism. They cultivate the 'good language', and at the same time contribute to setting the agenda in society."

The last few years Viestad has become more and more involved with farming. He has a small farm in the hamlet of Viestad in the Southern Norwegian town of Farsund, as well as an agricultural project in Elgin, near Cape Town, South Africa, named Garden of Elgin. The project is run in collaboration with Dr. Paul Clüver on the Cluver family estate, and features 50 different citruses, more than 40 varieties of peach, nectarine and apricots and a wide selection of herbs and vegetables, including more than 100 varieties of tomatoes. He also has a home in his birth town Oslo. Starting in 2010 Viestad is working on a new food and agriculture project, a center for food culture for children at Geitmyra Gård, a protected farm in the middle of Oslo, inspired by Alice Water's Edible Schoolyard.