Palmer was born and raised in Adelaide, South Australia. She is the only child of Kevin Palmer and Paula Sanders. Her parents divorced when she was three.
Palmer had been an extra on Deck Dogz (2005), and other films shot in Adelaide. At the age of 18, she was cast by filmmaker Murali K. Thalluri in the independent Australian film 2:37. Palmer portrayed Melody in the film, a popular high school student who becomes suicidal after being impregnated by her brother. She was nominated for the 2006 Australian Film Institute Award for Best Lead Actress for her performance. She then signed with a talent agent in Sydney. A role in Wolf Creek (2005) followed, in a pool party scene.
Palmer was cast to star with Tom Sturridge in her first American feature, Jumper, a science fiction film directed by Doug Liman. Her part was later recast when the lead characters were rewritten for older actors; her role went to Rachel Bilson. Palmer was devastated from losing the role and returned to Adelaide for a few months. She made her Hollywood feature film debut in The Grudge 2 in 2006, a horror sequel starring Amber Tamblyn and Sarah Michelle Gellar. Palmer described her character, Vanessa, as "the bitchy schoolgirl".
Palmer won the romantic lead in Disney's The Sorcerer's Apprentice, produced by Jerry Bruckheimer and directed by Jon Turteltaub. The film was based on the animated film Fantasia (1940), which was inspired by a poem by Goethe. Palmer stayed in Manhattan's West Village while filming for six months. She played Becky Barnes, a college student who is pursued by Dave Stutler (Jay Baruchel), a physics student and apprentice to the wizard Balthazar (Nicolas Cage).
In 2009, Palmer formed the film production company Avakea Productions, with Australian actresses Tahyna Tozzi and Nathalie Kelley. She was a guest judge on MTV Australia, for the Sydney filmmaking talent contest, Optus one80project. She also filmed an ad campaign that year for the Australian jean store, Just Jeans, and became the face and spokesperson for the Jurlique cosmetics company.
In 2011, Palmer starred in the sci-fi adventure film, I Am Number Four, alongside Alex Pettyfer and Dianna Agron. She played Number Six, one of nine aliens hiding out on Earth because her home planet was destroyed. Her character was skilled in martial arts, rode a Ducati motorcycle, and could become invisible and walk through fire. She went through stunt training for the role, learning to perform flips, swordfight, and do wirework. The film was adapted from a novel that was the first of a six-part series. Palmer signed on to do three movies, if the film became a franchise.
Palmer starred in the 2013 zombie film, Warm Bodies, produced by Summit Entertainment, and based on a young adult novel by Isaac Marion. She played Julie, a human who falls in love with a zombie (Nicholas Hoult). In February 2013, Palmer was announced as the "global face" of Artistry cosmetics. Palmer then starred in Love and Honor with Liam Hemsworth, an independent romance filmed in mid-2011 in Ann Arbor, Michigan. The film is set in the 1960s during the Vietnam War, and was released in March 2013.
Teresa recently married Mark Webber and gave birth to baby Bodhi on 17th February 2014.