Anupam Kher graduated from NSD and took a job as a lecturer at the Bharatendu Academy of Dramatic Arts in Lucknow. He responded to an advertisement recruiting teachers for an acting school in Bombay (now Mumbai) and was selected. He reached Bombay on 3 June 1981. The ad turned out to be fake, and he faced extreme hardship for a while, including homelessness and sleeping on railway platforms.

Anupam made his debut in Muzaffar Ali's Aagaman. He also acted in a small role in Utsav (released later). He auditioned for the role of Jawaharlal Nehru in Richard Attenborough's Gandhi. He was rejected for the role but later dubbed one dialogue in the Hindi version for ₹1,000. He was cast by Mahesh Bhatt in his breakout role as B.V. Pradhan, a 65-year-old retired teacher, while Kher was only 28. After being briefly replaced by Sanjeev Kumar, he aggressively confronted Mahesh Bhatt, who reinstated him for his raw passion. He won the Filmfare Best Actor Award.

He established himself as a top villain, most notably as Dr. Dang in Subhash Ghai's Karma (1986). The role of a fictional dictator, akin to the Bond villains from the 1960s, was a precursor to Mogambo from Mr. India, which came a year later. A specific scene where Dilip Kumar's character slaps him, leading the unhinged villain to wreak havoc and cause massacres, was especially popular. Around the same time came Rahul Rawail's Arjun (1985), where Anupam plays an evil political leader who hides behind a calm exterior. What made these roles seem all the more menacing is the fact that, unlike most villains those days, Anupam had a refined, genteel appearance that accentuated the evil in these characters. In this phase, he became one of the busiest actors in Bollywood, often shooting multiple films a day. He won his first Filmfare for Yash Chopra's Vijay.

He played an alcoholic, estranged father in Mahesh Bhatt's Daddy. He won a National Film Award (Special Jury) for this performance. Kher's sensitive performance as the guilt-ridden father who has been fighting a losing battle against alcoholism fetched him both audience affection and critical praise. Subhash Ghai's Raam Lakhan featured Anupam in one of his early popular comedic roles. His turn as Madhuri Dixit's father, a greedy shopkeeper who keeps getting fooled by his daughter's lover (played by Anil Kapoor), is hilarious. He also featured in Chaalbaaz, where he successfully blended hilarity with moral turpitude, playing a villain who also delivered laughs. His versatility in comedy began to be recognized. Kher won the Filmfare Award for Best Performance in a Comic Role for Ram Lakhan. Ghai and Kher continued to work in several films together. He acted in Yash Chopra's Lamhe, cementing a long personal and professional association with the director. Many years earlier, as a newcomer, Anupam sought a role in Chopra's film Mashaal and was turned down, but the director promised him an appropriate role in the future. Kher won the Filmfare Award for Best Comedian for Lamhe. In 1992, he starred in Chopra's Darr alongside Shah Rukh Khan, Sunny Deol, and Juhi Chawla, a role that won him his seventh Filmfare Award.

Anupam was featured in Suraj Barjatiya's Hum Aapke Hain Koun, one of India's biggest box office draws till that point in time. During the shoot, he was diagnosed with facial paralysis (Bell's palsy), but continued to shoot despite the affliction. He played Shah Rukh Khan's liberal father in Dilwale Dulhania Le Jayenge (1995), a role that redefined father figures in Hindi cinema, particularly through an improvised scene where Dharamvir joyously celebrates his son's academic failure rather than scolding him (akin to Kher's father in his own life). Kher incorporated personal touches into the role, such as referencing his real-life uncle while introducing Raj to his ancestors in a quirky picture gallery scene, and he won the Filmfare Award for Best Performance in a Comic Role for the act. In 1998, he famously featured in Karan Johar's debut Kuch Kuch Hota Hai as Principal Malhotra, in a comedic bit with Ms. Briganza (played by Archana Puran Singh) where his character says, “You are very queet” (cute). This specific dialogue was drawn from Kher's real life; during his college days in Shimla, a girl he had a crush on complimented his acting as “very cute,” which he mispronounced at the time as “queet,” a memory he incorporated into the film to great comic effect. In 1999, Anupam Kher ventured into production with Rituparno Ghosh's Bengali film Bariwali, which won two National Film Awards (Best Actress for Kirron Kher and Best Supporting Actress for Sudipta Chakraborty).

Anupam featured in Mohabbatein (2000) and Hrithik Roshan's debut Kaho Naa… Pyaar Hai (2000). He groomed and mentored Abhishek Bachchan as an actor, in addition to starring alongside him in Refugee (2001). In 2002, Anupam debuted as a director with Om Jai Jagadish (2002), a family drama featuring Anil Kapoor, Abhishek Bachchan, Fardeen Khan, and Urmila Matondkar. He made his international breakthrough in Bend It Like Beckham (2002). He served as Chairman of the National School of Drama (2001–2004). He was awarded the Padma Shri in 2004.

Anupam founded the acting school Actor Prepares (2005). He premiered his autobiographical one-man play Kucch Bhi Ho Sakta Hai (2005). He produced and starred in Maine Gandhi Ko Nahin Mara (2005), playing a professor with dementia. He received a Special Mention at the National Film Awards for the film. He played Kamal Kishore Khosla in a small-budget film, Dibakar Banerjee's Khosla Ka Ghosla (2006), which became a cult classic and won the National Award for Best Feature Film. He appeared in Ang Lee's Golden Lion-winning film Lust, Caution (2007). He played Police Commissioner Prakash Rathod in Neeraj Pandey's critical and commercial hit A Wednesday (2008).

Anupam Kher played Dr. Cliff Patel in the Oscar-winning film Silver Linings Playbook, working alongside Robert De Niro. The film received 8 Oscar nominations.

Anupam Kher was awarded the Padma Bhushan, India's third-highest civilian award, by the Government of India in 2016 for his significant contributions to Indian cinema and the arts. His 500th film The Big Sick was nominated for the Academy Award for Best Original Screenplay. In 2018, he began a lead role as Dr. Vijay Kapoor in the NBC medical drama New Amsterdam. He was nominated for a BAFTA TV Award for Best Supporting Actor for The Boy with the Topknot. In 2019, he portrayed former Prime Minister Dr. Manmohan Singh in The Accidental Prime Minister. He released his autobiography Lessons Life Taught Me, Unknowingly. In 2025, his second directorial venture Tanvi The Great was released and was shortlisted in 2026 among the top 200 films worldwide for Best Picture consideration.