In the letter, which Horovitz read, Yauch dedicated the honor to his fellow B-Boys, "who have walked the globe with me."
"To anyone who has been touched by our band, who our music has meant something to, this induction is as much ours as it is yours," said Yauch.
It was typical generosity from Yauch, the gravelly-voiced rapper who helped make the Beastie Boys one of the seminal groups in hip-hop and whose good-hearted nature led him to humanistic causes and made him beloved in hip-hop. One of his most famous rhymes was a sweet ode to women, which he called "long overdue": "To all the mothers and sisters and wives and friends/ I want to offer my love and respect to the end."
When the news came Friday that earlier that morning, Yauch, 47, had died after a nearly three-year battle with cancer, the words from his letter felt particularly apt. The outpouring of sadness at the loss, and celebration of the music Yauch helped created, was immediate and vast, shared across social media by those close to him, rappers influenced by "Paul's Boutique" and hip-hop listeners raised on Beastie Boys videos.
The rapper Q-Tip, a member of another major New York hip-hop group, A Tribe Called Quest, recalled that the Beastie Boys "showed us the ropes." Sean "Diddy" Combs called Yauch "a true pioneer and a creative force who paved the way for so many of us." The rapper Nas lamented the loss of a "brother": "MCA was so cool," he said.
For Eminem, Yauch was an undeniable touchstone: "I think it's obvious to anyone how big an influence the Beastie Boys were on me and so many others."
Yauch was an integral, founding member to the ever-weaving trio: three Jewish kids from New York who found widespread respect in a hip-hop world with few credible white performers.
In a span of more than a quarter century that covered four No. 1 albums and more than 40 million records sold, the Beastie Boys played both prankster and pioneer— a simultaneously goofy and groundbreaking act that helped bring hip-hop to the mainstream.
The demure, gray-haired Yauch wasn't the most boastful B-Boy; he was the thoughtful one and a steady source of the trio's innovative spirit. A practicing Buddhist, he led the group in performing concerts to benefit Tibet and, as a filmmaker, he helped create their imagery.
"The group's music crossed genres and color lines, and helped bring rap to a wider audience," said Neil Portnow, president of the Recording Academy. "Yauch was an immense talent and creative visionary."
Adam Nathanial Yauch, born in Brooklyn, formed the Beastie Boys with high school friend Diamond. Originally conceived as a hardcore punk group, they played their first show on Yauch's 17th birthday.
In the letter read at the Rock and Roll Hall of Fame induction, Yauch recalled their early days at his parents' home in Brooklyn, "where we used to practice on hot Brooklyn summer days after school, windows open to disturb the neighborhood."
The group became a hip-hop trio soon after Horovitz joined and coalesced after Yauch dropped out of Bard College two years into his studies. They released their chart-topping debut "Licensed to Ill" in 1986, a raucous album led by the anthem "(You Gotta) Fight for Your Right (To Party!)".
It was the first hip-hop album to top the Billboard chart, and while it remains popular, its irreverent rock-rap fusion bore few hints of an act with staying power.
"Adam was incredibly sweet and the most sensitive artist, who I loved dearly," Russell Simmons, whose Def Jam label released "Licensed to Ill," said on his website.
In the seven studio albums that followed, the Beastie Boys expanded sonically and grew more musically ambitious.
Their follow-up, 1989's "Paul's Boutique," ended any suggestion that the group was a one-hit wonder. Extreme in its sampling and thoroughly layered, the album (produced by the Dust Brothers) was ranked the 156th greatest album ever by Rolling Stone magazine in 2003.
The Beastie Boys would later take up their own instruments — a rarity in hip-hop — on the album "Check Your Head" and subsequent releases. Yauch played bass. Later, they would even release an album of instrumentals, which won one of their three Grammys in 2007.
On "Pass the Mic," he rapped: "If you can feel what I'm feeling then it's a musical masterpiece / If you can hear what I'm dealing with then that's cool at least / What's running through my mind comes through in my walk / True feelings are shown from the way that I talk."
For many, the Beastie Boys' lyrics — overflowing torrents of wit, humor and rhyme — were always the main draw. While other forms of hip-hop celebrated individualism, the Beastie Boys were a verbal tag team. Yauch once rapped, "on the tough guy style I'm not too keen."
Their popularity perhaps peaked with 1994's "Ill Communication," which spawned several of their most famous music videos, including "Sure Shot" and the Spike Jonze-directed "Sabotage" — a hit highlighted by Yauch's bass solo. (MTV, which played a key role in the Beasties' rise, hurriedly assembled an hour-long tribute show to Yauch on Friday night.)
Yauch used the group's growing fame to attract awareness for Tibetan Buddhists. He founded the Milarepa Fund to promote activism for Tibet in defense of what the nonprofit considered China's occupational government.
In 1996, Yauch and Milarepa produced a hugely popular benefit concert for Tibet in San Francisco, which was followed by more international concerts over the next decade.
"He was a goofball and behind a lot of their prankiness, but if you wanted to talk to him about what was going on in the world and social issues and everything, you got a totally different guy," said Rick Krim, executive vice president of music and talent relations at Vh1.
Introducing the group at the Rock Hall, Public Enemy rapper Chuck D said the Beastie Boys "broke the mold."
"The Beastie Boys are indeed three bad brothers who made history," Chuck D said. "They brought a whole new look to rap and hip-hop. They proved that rap could come from any street — not just a few."
Yauch also went under the pseudonym Nathanial Hornblower when working as a filmmaker. He directed numerous videos for the group, as well as the 2006 concert film "Awesome: I F-----' Shot That!" (shot entirely by fans given cameras) and the basketball documentary, "Gunnin' for that (No.) 1 Spot."
In 2008, he co-founded the noted independent film distribution company Osciolloscope Laboratories, named after his New York studio.
Yauch is survived by his wife, Dechen Wangdu, and his daughter, Tenzin Losel Yauch.
Yauch's illness, about which he first expressed hope that it was "very treatable," forced the group to cancel shows and delayed the release of their last album, "Hot Sauce Committee, Pt. 2." He hadn't performed in public since 2009.
But the enduring popularity of the Beastie Boys across some 28 years is one of the steadiest paths of success in pop music — a time remarkable for the constant, warm camaraderie between Yauch, Horovitz and Diamond.
"They are truly rock's most realized group — not hip-hop but all music, really," wrote Questlove, the drummer for the Roots, who toured with the Beastie Boys. "I mean, did we really expect the most thoughtful, mature, considerate act in music to be the same brats who gave us 'Licensed To Ill'?"
AP Music Writer Nekesa Mumbi Moody and AP writer Mesfin Fekadu contributed to this report.