The star died from lymphoma at a hospice in Tampa, Florida on Friday (22Jul11).
Aldredge was a regular on stage and screen, appearing in films like Cold Mountain in 2003 and The Assassination of Jesse James by the Coward Robert Ford in 2007.
He appeared on hit TV series The Sopranos and Boardwalk Empire and co-starred with Glenn Close on two seasons of legal drama Damages.
He also earned a Daytime Emmy Award in 1978 for Outstanding Individual Achievement in Children's Programming for his role on Henry Winkler Meets Shakespeare; an episode aired as part of The CBS Festival of Lively Arts for Young People.
A celebrated Broadway star, Aldredge also starred in more than 28 stage productions including The Crucible, Twelve Angry Men and Tom Sawyer.
He landed a total of five Tony Award nominations throughout his stage career for performances in shows such as Sticks and Bones (1972), Stephen Sondheim musical Passion (1994), and Twentieth Century (2004).
He also starred opposite the late Dame Elizabeth Taylor in The Little Foxes in 1981.
Emergency services were called to Steinbrenner's Tampa, Florida home on Monday night (12Jul10) and he was admitted to St. Joseph's hospital, where he was reported to be in an "extremely critical condition".
He passed away at around 6.30am (EST) on Tuesday morning (13Jul10), according to the Associated Press.
His death comes just days after he celebrated his 80th birthday on 4 July (10) and two days after longtime Yankees Stadium public announcer Bob Sheppard died at the age of 99.
In a statement, the Steinbrenner family says, "He was an incredible and charitable man. He was a visionary and a giant in the world of sports. He took a great but struggling franchise and turned it into a champion again."
Steinbrenner took over the Yankees in 1973 and the baseball team has won 11 pennants and seven World Series under his ownership, the longest in club history.
Outside the world of sport, Steinbrenner was known for being lampooned, with his permission, on hit TV comedy Seinfeld, when character George Costanza - played by Jason Alexander - worked for the Yankees.
Lee Bear portrayed Steinbrenner, although the character's face was never seen and he was always shot from behind at his office desk at Yankee Stadium. Larry David provided Steinbrenner's voice and the caricature depicted the mogul as a talkative man known for his bad decisions, who sometimes referred to himself as "Big Stein".
Steinbrenner's other TV appearances include a hosting gig on U.S. sketch show Saturday Night Live in 1990, and a movie cameo in Brendan Fraser's 1994 baseball film The Scout. He was referenced in a 1992 episode of The Simpsons, titled Homer at the Bat.
His personal fortune was estimated at a staggering $1.6 billion and he used his cash to invest in six Broadway plays in the 1960s and '70s, including the Tony Award-nominated musical Seesaw in 1974.
Steinbrenner is survived by his wife Elizabeth Zieg and their four children - Hank, Hal, Jessica and Jennifer.