Hansen was School Captain of The Hills Grammar School in Kenthurst, New South Wales and is a graduate of the University of Sydney with honours in Australian literature and Australian history.
In 1996 he appeared as a subject in Simon Target's documentary Uni about three students studying at the University of Sydney (Hansen later satirised Target in CNNNN where he played the network's British correspondent who was also called Simon Target). Soon-to-be fellow Chaser member Charles Firth was one of the other two students featured. During the documentary it was revealed that Hansen suffered from clinical depression while attending the university.
Hansen starred in The Chaser's satirical American news show CNNNN as the leader of the "newsband". He was also characters Rudi J Blass, director of "Newstainment", and Simon Target, an English reporter. Hansen's performance in the first season of CNNNN earned him the Australian Comedy Award for Outstanding Television Newcomer.
Hansen has been a regular writer and performer on The Chaser's War on Everything since the pilot episode. He is particularly known for composing and performing songs on the program. He is also known for his character pieces, which include Scenes from the Life of the Crazy Warehouse Guy, The Surprise Spruiker, Clive the Slightly Too-Loud Commuter, and Mr. Ten Questions. In the second part of the first season and the whole of the second and third, Andrew sported a different hairstyle every week. He has said that he likes to look entertaining with his clothes and his hair.
Hansen is a pianist and guitarist and in addition to his songwriting, Hansen composed the show's theme music, which received the APRA-AGSC Screen Music Award for Best Television Theme (2006).
In The Chaser's War on Everything DVD Volume 2's commentary, Hansen revealed that he is a fan of computer games and Doctor Who. This may have sparked the inspiration for one of his songs sung on The Chaser's War on Everything Season 1, about Doctor Who. It is also stated on the commentary that about 3/4 of the Doctor Who props in the video clip were supplied by Andrew himself. On the Season 2 Volume 1 commentary, it was revealed jokingly that Hansen is a huge fan of U2, which is why he chose not to imitate lead singer Bono during a sketch. This allegation was possibly tongue-in-cheek, as Hansen did make fun of Bono by playing a Bono-like character in his radio show The Blow Parade.
For Season 1 of the program, he received the Australian Film Institute Award for Best Performance in Television Comedy (2006).
The most controversial song that Hansen has performed was The Eulogy Song, which was originally written for Chris Taylor's play Dead Caesar, with music by Hansen and lyrics by Taylor. On 17 October 2007 episode of The War, Hansen performed the song which satirised the lives of several deceased celebrities, including Peter Brock, Stan Zemanek, Princess Diana, Donald Bradman, Steve Irwin, John Lennon, Jeff Buckley and Kerry Packer, expressing the view that people with flaws during life are often disproportionately hailed as "top blokes" after death. The song became the target of significant media attention, with several radio and television personalities saying the song was in "bad taste", and both the then Prime Minister of Australia John Howard and then Leader of the Opposition Kevin Rudd expressing negative views.
The members of The Chaser are running Giant Dwarf, a theatre in Sydney for regular comedy and storytelling shows featuring various performers. It opened in February 2014.
Hansen co-wrote and appeared in the live show Cirque du Chaser, which toured Australia in 2005.
Hansen composed and performed the music for the Sydney Theatre Company's 2007 musical comedy Dead Caesar, which was written by Chaser colleague Chris Taylor. He also played the roles of Marc Antony and Lucius. The Eulogy Song was originally written for and performed during this play.
In 2008, Hansen toured Australia with The Chaser's second stage show, The Chaser's Age of Terror Variety Hour.
In October 2009, Hansen hosted The Goodies: Before, During and After, a live show by British comedy trio The Goodies at Sydney's Riverside Theatre (Parramatta) and at the World's Funniest Island comedy festival. The show involved Hansen interviewing Tim Brooke-Taylor and Graeme Garden, as well as performing a Goodies song with them.
In 2011, Hansen joined various combinations of The Chaser team's members for a series of live shows in Sydney entitled The Chaser's Empty Vessel.
In 2014, Hansen and Chris Taylor toured Australia with a revue show of new songs and sketches entitled One Man Show. In 2015, they toured In Conversation with Lionel Corn, a parody of writers festival sessions.
Hansen was the guitarist and one of the vocalists for independent Sydney band The Fantastic Leslie. The Fantastic Leslie was composed of Cameron Bruce, Tom Gleeson, James Fletcher and Hansen. In July 1999 the band released their 6-track EP A Tiny Mark which was distributed through MGM Distribution. He was also a member of independent alternative band Mending.
Hansen co-wrote the short film Garbage Man with Charles Firth and British comedian Henry Naylor. It was a Tropfest finalist in 2005 and a prizewinner at Germany's Ohne Kohle festival. Hansen has also been known to feature on the musical comedy circuit, including a recorded performance of one of his more famous songs, 'I Wish I Was A Scottish Stand-Up Comedian', for the Laugh-A-Poolooza 2006 DVD release.
Hansen has had writer/performer contributions to the Nine Network's Comedy Inc. and the ABC's My Favourite Album. He has performed occasional voice-overs for ABC programs including First Tuesday Book Club and Media Watch. He composed the music for Nickelodeon's Sarvo and Napman, and songs for the Sesame Street character Ollie. Hansen appeared and presented at the 2007 MTV Australia Awards and the 2007 and 2011 ARIA Music Awards. In 2007, he made a guest appearance on Nine's The Nation. In 2008, he appeared in a sketch on SBS's Newstopia, as well as an episode of the Australian gaming TV show Good Game on the ABC, challenging the hosts to a 'Roffle Cup'. He also made an appearance as a guest host on the program in 2010, filling in for host Steven O'Donnell, again in 2011 filling in for host Stephanie Bendixsen and 2012 filling in for O'Donnell. He also made an appearance as a special guest in Good Game 10th year birthday special in 2016. In 2009, he made guest appearances on Network Ten's Rove and Good News Week. He appeared again on Good News Week in 2010, this time with Chris Taylor, in the guise of characters from their radio show The Blow Parade. The same year, he was a guest on Top Gear Australia, where he drove deliberately slowly around the celebrity track for humorous effect.
Hansen was the host of Strictly Speaking, a speechmaking competition series, which aired on ABC1 in 2010.
He was a producer and regular panellist on the comedy show The Unbelievable Truth, a TV version of the BBC Radio 4 program of the same name. It aired on Australia's Seven Network in 2012.
He composed the music for and starred in The Blow Parade, a scripted radio comedy series he made with Chris Taylor. It premiered on triple j on 28 April 2010. The series was released on CD and through the iTunes Store with bonus tracks. This album won the 2010 ARIA Award for Best Comedy Release.
He played the character 'Dex' in the 3D movie Sanctum, produced by Andrew Wight and released in 2011. Hansen has worked with Benjamin Maio Mackay twice, once on stage in 2016's Great Detectives of Old Time Radio Live and again in 2017 as a supporting role in the audio drama adaptation of The Phoenix Files.