Ives starred on Broadway as Cap'n Andy in the 1954 Broadway revival of "Showboat" and the following year created his signature role of Big Daddy Pollitt for the original Broadway production of Tennessee Williams' "Cat on a Hot Tim Roof", helmed by Elia Kazan, who also directed him as Sam the sheriff in the feature "East of Eden" (1955). After playing himself in Kazan's "A Face in the Crowd" (1957), he enjoyed his peak year in the business, appearing in four substantial features in 1958. He portrayed Ephraim Cabot, the cuckold of Sophia Loren, in "Desire Under the Elms" and Cottonmouth, the outlaw hunter of Nicholas Ray's "Wind Across the Everglades". He also reprised Big Daddy for Richard Brooks' film version of "Cat on a Hot Tin Roof" and won a Best Supporting Actor Oscar for his rough but fair-minded ranch owner Rufus Hannassey in William Wyler's "The Big Country". Other memorable feature roles from this period include his villainous turn in Andre de Toth's "Day of the Outlaw" (1959) and his stint as the captain in "Ensign Pulver" (1964).
Though often the big baddie for film, his troubadour persona was just the opposite as he earned the reputation of a sweet, gentle giant, singing songs like "The Big Rock Candy Mountain" and "I Gave My Love a Cherry". He narrated the Christmas cartoon perennial "Rudolph the Red-Nosed Reindeer" (NBC, 1964), singing its title song and others, and became more recognizable for his TV work during subsequent decades. His TV series debut came as Prater Beasley in NBC's "Daniel Boone", and he played the title role of the short-lived ABC series "O.K. Crackerby" (1965-66), as well as Walter Nichols in NBC's "The Lawyers", seen as one-third of the rotating segments of "The Bold Ones" (1969-72). He acted in two landmark miniseries, "Captains and Kings" (NBC, 1976) and "Roots" (ABC, 1977), and wrapped up his small-screen career as F W Woolworth in the miniseries "Poor Little Rich Girl: The Barbara Hutton Story" (NBC, 1987). Ives continually appeared in concerts around the world, singing for Golda Meir in Israel, a US President in Alaska and Queen Elizabeth II in a special command performance.