Ben Goldwasser and Andrew VanWyngarden formed the band while attending Wesleyan University during their freshman year. "We weren't trying to start a band," remarked Goldwasser. "We were just hanging out and showing each other music that we liked." They experimented with noise rock and electronica before settling on what Paco Alvarez of Spin calls "their current brand of shape-shifting psychedelic pop." The band formed under the name The Management, and two demo albums (We (Don't) Care and Climbing to New Lows) were unofficially released under the name, but since the name was already being used by another band, they later changed it to MGMT. While at Wesleyan, they were schoolmates of Francis and the Lights, with whom they have since toured. VanWyngarden and Goldwasser graduated in 2005 and toured extensively in support of the Time to Pretend EP released in the same year, opening for indie pop band Of Montreal.

In the autumn of 2006 Maureen Kenny signed the band to Columbia Records. When the band received a call from the A&R department of Columbia Records saying they were interested in their music, they thought it was a joke. The duo recorded with Flaming Lips/Sleater-Kinney music Producer Dave Fridmann in 2007 for their major label debut, Oracular Spectacular. MGMT opened for Of Montreal on tour in autumn 2007 as a five-piece touring band including Matthew Asti (bass), James Richardson (drums), and Hank Sullivant (guitar). In November 2007, they performed for the first time in Europe, supporting the band Samantha and The Courteeners at Koko in London, England. After March 2008, Hank Sullivant left the band to pursue his own band, Kuroma. Will Berman joined as the new Drummer, James Richardson switched from drums to guitar, and Matthew Asti remained on bass.

On October 5, 2007, Spin named MGMT "Artist of the Day." In November Rolling Stone pegged MGMT as a top ten "Artist to Watch" in 2008. The band placed ninth in the BBC's Sound of 2008 Top Ten Poll. They were also named as Last.fm's most played new Artist of 2008 in their Best of 2008 list. At the 51st Grammy Awards, the Justice remix of "Electric Feel" won the Grammy Award for Best Remixed Recording, Non-Classical. The group was nominated for the Grammy Award for Best New Artist and "Kids" was nominated for Best Pop Performance by a Duo or Group with Vocals at the 52nd Grammy Awards..

The band supported Radiohead on the Manchester date of their world tour and went on a headline tour of the UK during November 2008, playing at venues such as Manchester Academy and Shepherd's Bush Empire. MGMT opened for M.I.A. on the Vassar College date of her 2008 tour, and also played several shows with Beck during his 2008 tour. They appeared at the 2008 and 2009 editions of the Bonnaroo Music Festival. Bruce Springsteen was in attendance during their 2009 Bonnaroo late-night set, which followed his headlining appearance on What Stage. They also toured Australia with a headlining spot on the Meredith Music Festival line-up. The group played a show at the Virgin Music Festival on the Toronto Islands on September 6, 2008, playing nine songs off their Oracular Spectacular album. They also played the 2008 Street Scene festival in San Diego, California. On February 27, 2009, MGMT performed alongside Spectrum at The Dome in Finsbury Park. MGMT also played another show in Australia at the 2009 Splendour in the Grass Festival. They headlined this music festival along with other well known bands such as Bloc Party, The Flaming Lips, Happy Mondays, and Jane's Addiction. MGMT opened for Paul McCartney, an admitted fan, at Fenway Park in Boston, Massachusetts, on August 5 and 6, 2009. On August 15, 2009, MGMT played in Hamburg, Germany, at the Dockville Festival and performed several songs from their upcoming album. MGMT was one of the headlining bands for the Treasure Island Music Festival on Treasure Island in San Francisco, California, on October 17, 2009.

During production of Congratulations in 2009, VanWyngarden and Goldwasser met with Lou Reed, the former lead singer and Guitarist of The Velvet Underground, about contributing vocals to "Lady Dada's Nightmare". VanWyngarden recalls, "he pretty much said it didn't need it. And then he also talked about how we didn't need managers."

On August 25, MGMT released a music video for "Congratulations", the third video of their second album. MGMT was one of the third tier bands for the 2010 Coachella Festival in Indio, California. The event draws nearly 120,000 attendees annually. On October 31, 2010, the band performed for the Voodoo Experience in New Orleans, Louisiana. The band decided to dress as the main characters from Scooby-Doo for Halloween; Andrew dressed up as Daphne and Ben dressed up as Velma. They headlined at Fun Fun Fun Fest which was held at Waterloo Park in Austin, Texas on November 6, 2010. The performance was the last show in the US for MGMT in 2010. Their first 2011 gig was at Mar del Plata, Argentina, in front of a crowd of more than 40,000 on the beach in a free event which they headlined. MGMT began their first Asian tour on February 22, 2011. On September 22, 2011 MGMT performed the Pink Floyd song "Lucifer Sam" during Late Night with Jimmy Fallon's "Pink Floyd Week".

In January 2012, MGMT confirmed in an interview with Intercourse Magazine that they had started work on their third album, with VanWyngarden stating that he had written five songs. On February 27, 2012, MGMT began recording the album with Dave Fridmann at his Tarbox Road Studios. In March 2012, VanWyngarden said that MGMT will perform new songs on their upcoming shows in Latin America. On March 30, 2012, the band premiered a new song, entitled "Alien Days", at a show in Bogotá, Colombia. The band performed on August 3, 2012 in Montreal, Quebec, Canada at Osheaga, and on August 5, 2012 in Bethlehem, Pennsylvania, US at Musikfest. In January 2013, NME and Rolling Stone published an interview in which the band announced that the album was tentatively scheduled for a June 2013 release. As of March 2013, the process of recording the album at Tarbox Road Studios with Fridmann was near completion.

They have collaborated with the Rapper Kid Cudi, and are featured on one track – "Pursuit of Happiness" from his album Man on the Moon: The End of Day. For the 2010 MTV VMA's Kid Cudi was nominated for Best Hip-Hop video for "Pursuit of Happiness" a track which features MGMT and Ratatat. They also collaborated on the track "Worm Mountain" on The Flaming Lips' Embryonic.

Will Berman stated in an interview with HitFix in April 2015 that "We've been taking a little break I guess. We've been at it for years at this point. There's more to come." He didn't want to speak for either Ben or Andrew on when there would be a new album from the group. On December 26, 2015, the band tweeted announcing that they would return in 2016. As of at least October 1, 2016, the band has been working on an untitled new album. On May 8, 2017, the band released a teaser video on Instagram alongside the title of the forthcoming album as Little Dark Age, following a series of cryptic tweets the week prior. On June 21, the band revealed that their next album is finished. On October 17, the band released "Little Dark Age", the title track from their new album and their first single in four years. "When You Die" was released as the second single on December 12, 2017. The third single from the record, "Hand It Over", was released on January 5, 2018.

Little Dark Age is both an expression of surprise and dismay to the current political and social climate with an occasional reference to their own personal lives. The election of Donald Trump as President of the United States is where the inspiration came. Of the election, VanWyngarden stated, "We were like, 'Wow, is it actually possible for the most impossible thing to happen? [...] Apparently, we were more inspired to write pop music after evil took over the world." Touring Guitarist, James Richardson, also provided great inspiration, which resulted in the song 'James' being dedicated to celebrate the band's friendship. The album was released on February 9, 2018 with an upcoming North American tour.