Ianucci’s American political comedy Veep has been nominated for best comedy or musical on TV.
Outlander was short listed in three categories.
Caitriona Balfe, who plays the lead role of time-crossed nurse Claire Randall in Outlander, has been nominated for best actress in a TV series or drama.
Her fellow Outlander actor, Tobias Menzies, has been nominated for best actor in a limited series or TV movie.
Outlander itself, based on the hugely successful books by Diana Gabaldon which mix historical fiction with romance and time travel, has been shortlisted for Best TV Series or Drama, alongside Empire, Game of Thrones, Mr Robot and Narcos.
Outlander, possibly the biggest TV series ever shot in Scotland, is based at a production studio in Cumbernauld and has been shot across the country.
Sam Heughan, the Scottish actor who plays the main male role in the series, Jamie Fraser, missed out on a nomination this year.
Cumming appeared to be surprised by his nomination and said on the social media platform Twitter: “Holy Cow! I just got a Golden Globes nomination!”
Ianucci used the same medium to say: “Hurrah to the whole [Veep] cast and crew on our Golden Globe nomination. Outstanding, team!”
The Hollywood Foreign Press Association will hand out the awards at a January 10 ceremony in Los Angeles hosted by comedian Ricky Gervais
Overall the drama Carol leads the Golden Globe nominations with five nods, including the top category for best drama, while Wall Street movie The Big Short leads the comedy film categories with four nominations.
Carol, the story of a married older woman who falls in love with a young shopgirl in the 1950s, will contend for best drama opposite Leonardo DiCaprio movie The Revenant psychological thriller Room, Spotlight and the action thriller Mad Max: Fury Road, which was produced by Scot Iain Smith.
Carol’s lead stars Cate Blanchett and Rooney Mara both landed best actress nominations, and the movie also picked up nods for director Todd Haynes and for best original score.
The Big Short, which takes look at the housing bubble crash that led to the 2008 recession, will contend for best comedy/musical film alongside space adventure The Martian, Spy, coming-of-age comedy Trainwreck and Joy.
Last year’s Golden Globe best comedy/musical film winner, Birdman went on to win the best picture Oscar.