Batmanglij was born to Iranian parents, and grew up in Washington, D.C. His mother is cookbook author Najmieh Batmanglij while his Father is a publisher. His parents arrived in D.C. in 1983. His brother is independent filmmaker Zal Batmanglij. The two collaborated on the film Sound of My Voice, which Rostam scored and which Zal directed and co-wrote. Rostam also composed an original piece for piano that was featured in Zal's film The East.
Batmanglij majored in music at Columbia University where he joined the band Vampire Weekend in 2006. "At Columbia, I would study classical harmony in classes and I would study music on my own, and I would try to re-create songs that I love in recordings...that was really how I learned." The name of the group comes from the movie of the same name that bandmate Ezra Koenig and his friends made over summer vacations. Batmanglij produced their self-titled debut album shortly after graduation while concurrently working multiple full-time jobs. He also produced the band's follow up album, Contra, which sold 124,000 copies in its first week and landed atop the Billboard 200 charts. Batmanglij plays guitar, keyboard and sings in the band but also acts as a lyricist and Songwriter, co-writing the song "Diplomat's Son" on Contra. Koenig has described himself and Batmanglij as "the two main songwriters in the band."
Batmanglij began recording with Ra Ra Riot's vocalist Wes Miles on a project which was later to become Discovery. They released their debut album LP on July 7, 2009 on XL Recordings. The album features guest vocal contributions from Koenig as well as Dirty Projectors' Angel Deradoorian.
In 2010, Converse released "All Summer", written by Batmanglij and featured Kid Cudi and Bethany Cosentino from Best Coast.
In September 2011, Batmanglij released a solo track called "Wood". Timeout Chicago's Brent DiCrescenzo gave the song 4 out of 5 stars and wrote that "his voice pleasantly recalls a drowsy David Byrne". On November 1, 2011, Zane Lowe debuted another a solo song sung by Batmanglij called "Don't Let it Get to You" as the Hottest Record in the World on BBC Radio1. The Fader referred to it as "a seismic event of a song." In January 2016, Batmanglij released the song "EOS" along with its music video which he had directed. On March 11, 2016, Batmanglij released the song "Gravity Don't Pull Me" along with its music video directed by Batmanglij and Josh Goleman. The video was filmed at The 1896 and features Dancers Jack Grabow and Sam Asa Pratt.
On March 18, 2013, Vampire Weekend released two songs from their album Modern Vampires of the City, "Diane Young" and "Step". Within two weeks each song had garnered more than 1 million views on YouTube. Music for both songs is credited to Batmanglij and Koenig, and lyrics are credited to Koenig. Modern Vampires of the City is the first Vampire Weekend album Batmanglij did not produce alone; for this record he collaborated with longtime friend Ariel Rechtshaid and the two co-produced the album together. It was released May 14, 2013.
Batmanglij produced and co-wrote two songs for The Walkmen frontman Hamilton Leithauser's solo album, Black Hours, which was released in June 2014. Also in 2014, Batmanglij produced two songs for singer Charli XCX. The song "Need Ur Luv" appears on her album Sucker and the song "Kingdom" featuring Simon Le Bon appears on The Hunger Games: Mockingjay, Part 1 – Original Motion Picture Soundtrack. In December 2014, Batmanglij along with Diplo and Ed Droste remixed Ty Dolla Sign's "Stand For" into a new song titled "Long Way Home". Batmanglij also wrote original music for a play by Kenneth Lonergan called This Is Our Youth, starring Kieran Culkin, Michael Cera, and Tavi Gevinson, which premiered on Broadway in 2014.
Batmanglij is openly gay and talked about his sexual orientation in the magazine Out. In an Instagram post in 2015, he said that Ed Droste of the band Grizzly Bear influenced his decision to publicly come out.
In 2016, he formed Hamilton Leithauser + Rostam with Hamilton Leithauser of The Walkmen. They released the single "A 1000 Times" in July 2016, which they performed on The Late Show with Stephen Colbert on September 12, 2016. Their song "In a Black Out" was featured in a commercial for the Apple iPhone 7. Their debut album, I Had a Dream That You Were Mine was released on September 23, 2016.
Batmanglij produced and co-wrote the song "Listen to Your Friends" from English singer Declan McKenna's debut album What Do You Think About the Car?, which was released in July 2017.