Wolk was born in Farmington Hills, Michigan, the son of Edie, an art teacher, and Robert Wolk, a shoe store owner. His family is Jewish, and Wolk was raised in Reform Judaism. During his teenage years, Wolk worked as an emcee at Bar and Bat Mitzvahs. He graduated from North Farmington High School in 2003, and from the University of Michigan School of Music, Theatre & Dance in 2007. Wolk is on the Board of Directors of the Brad Cohen Tourette Foundation. He also volunteers at "Camp Twitch and Shout," which is a camp for children (ages 7–17) with Tourette syndrome in Georgia.
In 2008, Wolk landed his first television role in Hallmark Hall of Fame's Front of the Class, as Brad Cohen. He subsequently played the title character in the 2009 ABC pilot Solving Charlie. In 2010, Wolk was cast as the lead in the Fox television series Lone Star, as Robert/Bob Allen, a Texas con man married to the daughter of one of his targets, while simultaneously maintaining a relationship in another town. The show was canceled by Fox after only two episodes.
Wolk had a role as Will in the romantic comedy movie You Again. Wolk played a presidential speechwriter named Andrew Pierce in Georgetown, a 2011 ABC pilot which did not go to air.
In Fall 2011, Wolk joined the second-season cast of the Showtime dramedy Shameless, with the recurring role of Adam. The second season premiered January 8, 2012. Wolk played the recurring role of Grant in three episodes of the ABC comedy Happy Endings, beginning with the first installment on February 8, 2012. In the summer of 2012 Wolk was featured in the USA Network mini-series Political Animals, starring Sigourney Weaver and Ciarán Hinds. Wolk played Douglas Hammond, the "good" son of a former President of the United States (Hinds) and the current Secretary of State (Weaver).
In 2013, Wolk joined the Season 6 cast of Mad Men, playing mysterious junior account man Bob Benson. As the season progressed, Benson became one of the most talked-about characters on the show. In the 2013-14 television season, Wolk was part of the cast of the CBS sitcom The Crazy Ones, starring Robin Williams and Sarah Michelle Gellar. Wolk plays a womanizing creative at the Chicago ad agency headed by Williams and Gellar, marking his second role as a worker at an ad agency after Mad Men.
In November 2014, Wolk was cast as the lead in the CBS summer drama Zoo, based on the novel by James Patterson and Michael Ledwidge. Zoo premiered in June 2015. Wolk played the role of Craig in movie Are You Joking? and that of Mike Penny in The Stanford Prison Experiment. In 2015, Wolk starred as Philip in the indie comedy movie This Is Happening. The movie about an estranged brother and sister who go on a road trip to find their runaway grandmother.
In 2016, Wolk starred as Brad in the thriller film Mercy, which was written and directed by Chris Sparling. In 2017, he guest starred as Craig Heidecker, an innovative young tech billionaire, in multiple episodes of Showtime's Billions.
In June 2015, he married Elizabeth Jae Lynch, during a ceremony that was held at Crossroads Estate, Firestone Winery in Los Olivos, California. They welcomed their first child, a boy, Charlie, in early 2017. He also went to Warner Middle School And North Farmington High School