Veep originated from Armando Iannucci's BBC series The Thick of It; his 2009 spin-off film In the Loop was even nominated for the Academy Award for Best Adapted Screenplay.

Before Veep, an American pilot adaptation of The Thick of It was made for ABC in 2007, directed by Christopher Guest and starring John Michael Higgins and Oliver Platt, but it was not picked up; Iannucci distanced himself from it, calling it 'terrible' with no improvisation or swearing.

Rhea Seehorn and Michael McKean both appeared in the failed 2007 ABC pilot of The Thick of It, and later both returned to appear in the seventh and final season of Veep.

Several actors from In the Loop, including Anna Chlumsky, Zach Woods, and Mimi Kennedy, became series regulars on Veep playing characters similar to but distinct from their film roles.

According to co-star Matt Walsh, Jonah Ryan was originally written as simply 'a fat, short, heavy smoker,' but the character was reshaped into his final form after Timothy Simons auditioned for the role.

The pilot was shot in Maryland in February 2011, and the series then filmed in Baltimore starting in October 2011, after months of rehearsal designed to help the cast get comfortable improvising together.

For its first season, Veep hired 978 local Maryland residents and generated an estimated $40 million for the state, per the Maryland Film Office; much of the show was shot on a soundstage built from a converted industrial warehouse in Columbia, Maryland, with replica sets of the Eisenhower Executive Office Building and the West Wing.

Starting with season 5, production moved from Baltimore to Los Angeles after Veep received California tax incentives; the show also filmed on location in Washington, D.C. for eight days in early 2016, including at Kramerbooks in Dupont Circle and the Spring Valley neighborhood where Julia Louis-Dreyfus once lived.

Creator Armando Iannucci stepped down as showrunner after season 4, citing the difficulty of fully dedicating himself to the show while juggling family life between Baltimore and London; David Mandel then took over as the show's first American showrunner.