Ivanek was born in Ljubljana, PR Slovenia, FPR Yugoslavia. He emigrated with his parents to the United States in 1960, when he was 3 years old. After a two-year stay, in 1962, the family moved back to Slovenia for five years and then returned to the United States in 1967. Having performed in numerous community theater plays in the San Francisco Bay Area, he graduated from Ellwood P. Cubberley High School in Palo Alto in 1975. Ivanek went on to graduate from Yale University in 1978 and afterward attended the London Academy of Music and Dramatic Art.
Ivanek has worked extensively on the stage. In 1982, he originated the role of Hally in Athol Fugard's play "Master Harold"...and the Boys. He has also appeared in the U.S. premieres of Caryl Churchill's Cloud Nine (for which he earned the 1981 Drama Desk Award for Outstanding Featured Actor in a Play) and Martin McDonagh's The Pillowman. He performs frequently on Broadway and has been nominated for three Tony Awards, for his performances in the original production of Brighton Beach Memoirs, in Two Shakespearean Actors, and in a revival of The Caine Mutiny Court-Martial, alongside David Schwimmer and Tim Daly. However, Ivanek is perhaps best known for his supporting roles in a number of well-known television series. The characters he portrays are most often professional men such as lawyers or government functionaries and are frequently antagonists. These roles include Emile Danko in Heroes; Roland in The X-Files; prosecuting attorney Ed Danvers in Homicide: Life on the Street; Ray Fiske in Damages; J.J. in Big Love; the Magister in True Blood; Governor James Devlin in Oz; and Blake Sterling, the Director of National Intelligence in the NBC drama series The Event.
He currently plays Russell Jackson, Chief of Staff, in the TV series Madam Secretary. He has also portrayed a broader range of roles, however, including John Dickinson, the Pennsylvania representative to the Second Continental Congress in the HBO miniseries John Adams. Ivanek has also guest starred on shows such as Law & Order: Special Victims Unit and House. He has appeared several times on Law & Order as both one-off characters and as Ed Danvers in crossover episodes with Homicide: Life on the Street. As well as his stage and television work, Ivanek has appeared in more than 20 feature films, including The Bourne Legacy, In Bruges, Dogville, Black Hawk Down, Donnie Brasco, Argo, and Seven Psychopaths. In 2012, he portrayed Dr. Stafford White in the Fox drama The Mob Doctor. As of 2014, he has supporting roles in several shows on broadcast and cable television, including the NBC drama series Revolution, where he plays the recurring roles of Dr. Calvin Horn and an illusory nanotech avatar of Horn; the USA Network drama Suits; the Cinemax drama Banshee; and the FX series The Americans. In That Guy... Who Was in That Thing, he reveals that his contract includes a rider to ensure that the character Ž in "Željko" does not appear as Z in the credits.