He attended Modern School in Delhi where he was part of the school cricket team. Azad, a nonconformist in many ways, was a stalwart allrounder for Delhi for years and in 95 Ranji Trophy matches he scored 4867 runs (47.72) and took 162 wickets (28.91). His highest score was 215 against Himachal Pradesh in 1985-86.

He was a surprise choice for the tour of Australia and New Zealand in 1980-81, he made his Test debut at Wellington. He then played three Tests without much success against England in 1981-82 and was then ignored till he was picked for the World Cup in 1983. Azad had his day in the sun when he played a leading part in India winning the semi-final against England, when he helped bottle up the middle order with his fastish off-breaks and earned a bonus while bowling the dangerous Ian Botham.

Azad also played a memorable innings against Pakistan in 1983 at New Delhi, in an exhibition day/night match. Pakistan batted first and made 197 runs for 3 wickets in 50 overs with Azad taking all 3 wickets. In India's reply, Kirti scored a rapid 71 not-out and steered India to a one-wicket victory. He hit seven sixes, including three consecutive sixes off Pakistani medium pacer Jalaluddin. But he met with no success in three Tests against Pakistan and West Indies and was discarded.

Later he followed his father Bhagwat Jha Azad, former Chief Minister of Bihar, into politics and was elected to Parliament on a Bharatiya Janata Party ticket from Darbhanga, Bihar. He is currently serving his third term in the Lok Sabha. He was previously an MLA from Delhi's Gole Market constituency. He won the 2014 Lok Sabha Elections from Darbhanga. On 23 December 2015 he got suspended from Bharatiya Janata Party for openly targeting Union finance minister Arun Jaitley over alleged irregularities and corruption in Delhi's cricket body Delhi and District Cricket Association.

Azad is married to Poonam and has two sons.^[8] His elder son Suryavardhan has played for Delhi Under-17s, Under-19s and Under-22s, while his younger son Somyavardhan has played for Delhi Under-15s and Delhi Under-17s.^[9][10]

His wife Poonam joined AAP Party on Nov 13, 2016, which she then quit on Apr 11, 2017 to join the Indian National Congress.^[11]

Following a 2012 sting operation on players of Indian Premier League (IPL), Azad came out in opposition of the tournament and demanded that it be banned.^[12] Speaking about the Indian T20 team, he reportedly alleged that the players played for self rather than the country. He further said that he felt agitated and ashamed to be associated with the BCCI in the wake of the IPL controversy.