Green was born in Philadelphia, Pennsylvania, the son of Barbara (nee Gesshel), an artist, and Herb Green, a math teacher. His first glimpse of fame occurred shortly after he was born, as his birth was used in a pamphlet on natural child birth.

Green was brought up Jewish and played a 1940s Jew in Woody Allen's movie Radio Days . In a 2000 interview he said "God is, to me, pretty much an idea. God is, to me, pretty much a myth created over time to deny the idea that we're all responsible for our own actions".

Green's first movie role was in the 1984 film, A Billion for Boris. He appeared in the 1987 film Can't Buy Me Love, playing the part of Patrick Dempsey's little brother, Chuckie Miller. He also starred in Woody Allen's Radio Days (1987) as Joe, and appeared in Big Business (1988) and, in the same year, in My Stepmother Is an Alien (with future Buffy co-star Alyson Hannigan). Green appeared in the miniseries It (as Richie Tozier, age 12), all three Austin Powers movies (as Dr. Evil's son, Scott), and Enemy of the State and The Italian Job as a computer specialist. He was also in the film Can't Hardly Wait and Without a Paddle.

Green's first television appearances were in Tales from the Darkside and Amazing Stories in the mid-1980s. He made a few appearances on the 1980s television series The Wonder Years. He also appeared in commercials as the window cashier for Rally's Hamburgers in the early 1990s, sparking the catch-phrase, "Cha-Ching!". In 1994 he starred alongside Jennifer Love Hewitt in the shortlived series Byrds of Paradise. Green also began appearing as Daniel "Oz" Osbourne the werewolf in the television series Buffy the Vampire Slayer during seasons 2-4. Green has also been featured in roles on Greg the Bunny, Tucker, The X-Files, That '70s Show, Will & Grace, Mad About Steve,Reno 911, Entourage, and Grey's Anatomy.

He is a co-creator and producer of the stop motion TV series Robot Chicken, for which he also does many voices and has even appeared in animated form. He also appeared as a cameo in the Fall Out Boy music video, This Ain't a Scene, It's an Arms Race, and in Weird Al Yankovic's White & Nerdy music video. In September 2007, he made an appearance on The Soup to imitate Chris Crocker. He also voiced the character of Joker, the pilot of the SSV Normandy, in the video game Mass Effect for the Xbox 360. He is a producer of The 1 Second Film and appears in the "making of" documentary that accompanies its feature-length credits. Green is also the co-creator (with Hugh Sterbakov) of the comic Freshmen, published by Top Cow Productions.