Anand was born in London, England, to Punjabi Sikh parents who migrated to the UK shortly after the partition of India. Her family, prior to the partition, originated from Khyber Pakhtunkhwa in present Pakistan.
Anand was privately educated at Bancroft's School, where contemporaries included Nina Mackay. Anand then entered King's College London in 1990 graduating with a BA in English in 1993.
After training as a journalist, Anand became European Head of News and Current Affairs for Zee TV, and one of the youngest TV news editors in Britain at the age of 25. She presented the talk show The Big Debate and was political correspondent for Zee TV presenting the Raj Britannia series – 31 documentaries chronicling the political aspirations of the Asian community in the most marginal constituencies in 1997. Until October 2007, Anand presented in the 10:00 pm till 1:00 am slot on Monday to Thursdays on BBC Radio 5 Live. She went on to co-present the station's weekday Drive (4:00-7:00 pm) slot with Peter Allen, having replaced Jane Garvey in 2007. Aasmah Mir replaced her when she left for maternity leave.
Anand has presented the BBC Radio 4 show Mid Week, and on television she has been a presenter on the Heaven and Earth Show. She has co-presented the Daily Politics on BBC Two with Andrew Neil from September 2008, with a break for maternity leave from January to September 2010.
Anand has also written articles for India Today and The Asian Age newspaper, and used to write a regular column in The Guardian ("Anita Anand's Diary", 2004–2005).
In July 2011 Anand left the Daily Politics to present a new show called Double Take on Radio 5 Live on Sunday mornings. In June 2012, Anand took over presenting Radio 4's Any Answers? Saturday current affairs phone-in programme between 2:00 and 2:30 pm from Jonathan Dimbleby who continues to present the phone-in's sister programme, Any Questions?
Anand's book Sophia: Princess, Suffragette, Revolutionary (about the Indian princess Sophia Duleep Singh, granddaughter of the last Sikh Maharani and Maharaja of Lahore, born in exile in England, who went on to struggle for causes including Indian independence, the welfare of Indian soldiers in the First World War and women's suffrage) was published in 2015. She also presented Sophia, Suffragette Princess, a 30-minute television documentary programme based on the book, which aired first on BBC One in late November 2015. She is co-author with William Dalrymple of Kohinoor: The Story of the World's Most Infamous Diamond (2017, Bloomsbury, ISBN 978-1-4088-8884-1).
On 18 November 2005, Anand won the Nazia Hassan Award for 2005 in the category of Upcoming Television Broadcasters.
Anand married science writer Simon Singh in September 2007. The couple have two sons, Hari and Ravi, and live in Richmond, London.