Conried was born Hans Georg Conried, Jr. in Baltimore, Maryland. His mother, Edith Beyr (née Gildersleeve), was a descendant of Pilgrims, and his father, Hans Georg Conried, Sr., was a Jewish immigrant from Vienna, Austria. He was raised in Baltimore and in New York City. He studied acting at Columbia University and went on to play many major classical roles onstage. Conried worked in radio before breaking into movies in 1939, and was also a member of Orson Welles' Mercury Theatre Company. He enlisted in the U.S. Army in September 1944 during World War II.

Conried appeared regularly on many radio shows during the 1940s and 1950s, notably the George Burns & Gracie Allen Show, on which he played a psychiatrist whom George regularly consulted for help in dealing with the dizzy Gracie.

Conried's most important single year was 1953, in which he made his Broadway debut in Can-Can and received screen credit in six films (among them The Twonky and The 5,000 Fingers of Dr. T). His other Broadway productions include 70, Girls, 70 and Irene.

Conried's inimitable growl and impeccable diction were perfectly suited to the roles he played, whether portraying the dim Professor Kopokin in the radio show My Friend Irma or portraying comic villains and other mock-sinister or cranky types, such as Captain Hook (and Mr. Darling) in Walt Disney's Peter Pan and The Grinch/Narrator from Dr. Seuss' Halloween is Grinch Night. According to the DVD commentary of Futurama, he was also the inspiration for the voice created for that series' "Robot Devil".

Conried also was a cast member of The Rocky and Bullwinkle Show, voicing the character of Snidely Whiplash in the Dudley Do-Right shorts and also hosted Fractured Flickers, another creation of Jay Ward and Bill Scott, as well as Wally Walrus on The Woody Woodpecker Show, Uncle Waldo P. Wigglesworth on Hoppity Hooper, and Dr. Dred on Drak Pack. He was well known as the Williams family patriarch, Uncle Tonoose, on the sitcom Make Room for Daddy, a role he played for 13 years. He was also a regular performer on the Jack Paar Tonight Show from 1959 to 1962.

Besides being the host of Fractured Flickers, Conried was a regular panelist on CBS's Stump the Stars. His many guest appearances included Davy Crockett, Meet McGraw, The Ray Milland Show, The DuPont Show with June Allyson, The Monkees, I Love Lucy (where he played English tutor Percy Livermore), The Many Loves of Dobie Gillis, Mister Ed, Ben Casey, Dr. Kildare, Lost in Space, The Beverly Hillbillies, The Lucy Show , Gilligan's Island, Have Gun – Will Travel, Love, American Style, Kolchak, Alice, Laverne & Shirley, The Love Boat, Hogan's Heroes, Match Game, Maverick and Fantasy Island. From 1956 until 1963 Conried made frequent guest appearances as Danny Williams' eccentric Lebanese "Uncle Tonoose" in Make Room for Daddy. In real life, Thomas was Lebanese, Conried was not.

Conried was active up until his sudden passing from cardiovascular disease on January 5, 1982. He was married to Margaret Grant from January 29, 1942 until his passing three weeks short of their 40th wedding anniversary. The couple had four children. His remains were donated to medical science.