Savage was born in Woodland Hills, California. Andrea is the daughter of Sharon Lee (Chrystie) and Richard Savage. Andrea’s paternal grandparents were Leonard Jay/James Savage and Florence Jane Kaplan (the daughter of Dorothy Silver). The surname “Savage” was originally “Shubkin”. Dorothy was the daughter of Barney Silver. Andrea’s maternal grandfather was Harry C. Chrystie (the son of Christo Chrystie and Slavrorila Yasilikos). Harry was born in Valtesiniko, Arcadia, Greece. Andrea’s maternal grandmother was Tillie/Lillie Groffman (the daughter of Isaac/Isaic Groffman/Grofman and Lillian Leah Solomon). Tillie was born in Massachusetts, to parents from Poland. Lillian was the daughter of Moishe Menke “Mordechai” Soloveitchik and Chaia Sarah. She is of three quarters Ashkenazi Jew and one quarter Greek descent (her maternal grandfather was of Greek origin). In her senior year of high school, she played Mame in Mame. She graduated from Cornell University where she majored in government with a minor in law studies. She has performed stand-up comedy at The Improv, The Comedy Store, The Ice House and other venues around Los Angeles.
Savage began her acting career playing Renata Vargas, the Brazilian exchange student on Sweet Valley High who befriends Jessica and Lila, while eventually falling in love with Todd Wilkins. Soon after she joined The Groundlings theater, performing weekly in their company. Savage received starring roles in Significant Others as Chelsea and in cult favorite Dog Bites Man as Tillie Sullivan. Soon after she starred in Step Brothers opposite Will Ferrell, following that with a comedy tour with Ferrell, Zach Galifianakis, Demetri Martin, and Nick Swardson. She also appeared with Woody Harrelson in The Grand (2008).
After taking time off to have her first child, in 2010 Savage reappeared in the film Dinner For Schmucks opposite Steve Carell and Paul Rudd. She also filmed two television pilots: The Strip created by Tom Lennon and Ben Garant for NBC and Wilfred, a dark Australian comedy being redone for FX. In addition, Savage created and starred in a series of shorts for the HBO show Funny or Die Presents about a very pregnant woman trying to engage in some casual sex, as well as a series entitled "Reenactments of Actual Conversations from the Ladies Rooms of Hollywood." She was also seen in the cult hit Party Down for Starz (Savage was originally cast as Casey Klein in the unaired pilot. Because she was pregnant, Lizzy Caplan took the role when the show went into production). Soon after, she wrote television pilots for Comedy Central, FOX studios, and NBC (produced by Jay Roach) as well as the screenplay Girls Weekend for Castle Rock Films. She also filmed opposite Hilary Swank in the film You're Not You. Her directorial debut was in 2012 when she shot her satirical PSA Republicans, Get in My Vagina! which she wrote and also stars in, alongside Kate Beckinsale and Judy Greer. This premiered on Real Time with Bill Maher on HBO and is one of Funny Or Die's most successful video shorts of all time.
In 2013, Andrea wrote a TV pilot for ABC/Sony produced by Jamie Tarses as well as another pilot for Comedy Central, River Dogs, produced by Will Ferrell's Gary Sanchez Productions. She also acted opposite John Leguizamo as "Juicy" in an untitled John Leguizamo pilot for ABC.
Savage's other television credits include starring roles in the FOX pilot Rebounding and Lies & The Wives We Tell Them To on NBC. Additionally, she has recently guest-starred on other popular comedies such as Modern Family, House of Lies, and The League.
Savage also starred alongside Danielle Schneider, Tymberlee Hill, Angela Kinsey, Kristen Schaal, and Casey Wilson in the Hulu original series The Hotwives. The series is a parody of the reality television franchise The Real Housewives on Bravo. Season one (The Hotwives of Orlando) focused on Orlando, while season two (now titled The Hotwives of Vegas) took place in Las Vegas with the same cast playing new characters.
In 2016, she began appearing as Senator (and later President) Laura Montez on Veep, who first appears as the running mate of the titular Veep's opponent, before ultimately becoming president in a complex manipulation of Constitutional procedure.
In 2017, she created the semi-autobiographical TruTV comedy I'm Sorry, which she also stars in. The series premiered on July 12, 2017.