The 6ft 5in star had been diagnosed with brain cancer and was in intensive care in New York before his death on Wednesday.
His son Rory said in a statement: "He was full of knowledge and kindness and goodness.
"He always wanted to share the great and beautiful things in life."
Herrmann played the beloved grandfather Richard Gilmore on Gilmore Girls, a waspish family drama set in a storybook Connecticut town.
Lauren Graham, who played Herrmann's on-screen daughter Lorelai Gilmore during the show's seven series, remembered the actor as the "kindest, classiest, most talented man" and said it was a "devastating blow to lose him".
"Ed Herrmann's combination of pure charisma plus his distinctive voice lit up any room he entered," she added.
"He had a gentlemanly manner, a wicked sense of humour, and a sharp wit. He was well-read, interesting, and just plain fun to be around."
Kelly Bishop, who played his wife Emily Gilmore, said she was "somewhat stunned" by his death, having only found out he was ill a few weeks ago.
"I think everyone who knew or worked with Ed found him to be absolutely delightful," she said in a statement. "Everything looks a little dim, as if the lights went down."
The actor, who trained at London's Academy of Music and Dramatic Art, was singled out for praise when Entertainment Weekly picked Gilmore Girls as one of its "new TV classics" in 2009.
Describing him as an "on-screen pro", it said he could "advise, hector, and soothe with debonair slyness".
But his son, Rory, said his father's favourite role had been US President Franklin D Roosevelt, whom he played in the TV movies Eleanor and Franklin and Eleanor and Franklin: The Whitehouse Years in 1976 and 1977.
The actor reprised the role in the 1982 movie musical Annie, and provided the voice for FDR in Ken Burns' documentary series The Roosevelts: An Intimate History, last year.
Herrmann also starred in Joel Schumacher's teen vampire film, The Lost Boys, alongside Kiefer Sutherland, where he played Max; and won a primetime Emmy in 1999 for his guest role in the Boston-based legal series The Practice.
His Broadway credits included the original run of Love Letters in 1989, The Deep Blue Sea with Blythe Danner in 1998 and George Bernard Shaw's Mrs Warren's Profession, for which he won a Tony Award in 1976.
He often appeared on the big screen in major films including The Wolf of Wall Street, The Aviator and Reds, and recently appeared on shows such as Grey's Anatomy, How I Met Your Mother and The Good Wife.
His manager Robbie Kass said in a statement: "Besides being an accomplished actor, [Herrmann] was also a true gentleman and a scholar, as well as being incredibly kind and decent man. He will be sorely missed."
Herrmann was surrounded by his family including his wife, Star, and three children when he died.
Actor Edward Herrmann, best known for his roles in TV show Gilmore Girls and vampire movie The Lost Boys, has died aged 71.