Upon its release, Two Suns was met with positive reviews from most critics. Additionally, it was shortlisted for the Mercury Prize in 2009, Khan's second nomination after Fur and Gold in 2007. On 31 July 2009, Two Suns was certified gold by the British Phonographic Industry (BPI), for shipments of 100,000 copies in the United Kingdom.
According to the accompanying press release, Two Suns is "a record of modern-day fables exploring dualities on a number of levels—two lovers, two planets, two sides of a personality", bringing reflection about "the philosophy of the self and duality, examining the need for both chaos and balance, for both love and pain, in addition to touching on metaphysical ideas concerning the connections between all existence." In Two Suns, Khan also presents an alter ego named Pearl, described by the press release as "a destructive, self-absorbed, blonde, femme fatale of a persona who acts as a direct foil to Khan's more mystical, desert-born spiritual self."
Two Suns received generally positive reviews from music critics. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album received an average score of 76, based on 32 reviews. Kevin Liedel of Slant Magazine called it "dark, but never needlessly so", and wrote that it "offers a rich, distinct world of subterranean lullabies, spacey timbres, and ghostly beauty." Mark Pytlik of Pitchfork Media called it a "significant step forward from her debut" and "home to some of the year's most thrilling music so far." Tim Chester of the NME described Two Suns as "a brilliant pop album", commenting that it is "epic in scope and ambition and requires a similarly epic patience to unravel its charms". Barry Walters of Spin wrote that "this art-rockJoan of Arc gushes duality motifs that thwart narrative but overflow with moonstruck sensuality."The A.V. Club's Sean O'Neal commented that "Khan's sublime voice easily distracts from any lyrical ponderousness, and it lends even lines about 'diamonds burning through rainbows' a dreamy sort of sense."The Guardian's Dorian Lynskey called it "fantastic as well as fantastical", noting that "[w]hereas her debut relied on charisma and imagination to paper over the songwriting cracks, [Two Suns] is agleam with striking melodies". Melissa Maerz of Rolling Stone felt that "[s]omehow, the music melts away the potential for hokeyness ... Khan proves she's a powerhouse under her billowy sleeves."
Allmusic's Heather Phares complimented Khan's "considerable skills at telling a story and setting a mood", but critiqued that the album's massive concepts and sounds require a little more time and patience to unravel to get to the songs' hearts. It's clear that Khan's talent and ambition are both huge".PopMatters' Erin Lyndal Martin felt that Khan "can do much better than some of the songs, which are weakened by synths, sophomoric lyrics, and sonic clutter." Martin continued, "While the weaker songs are definitely not throwaways, they miss the mark in more than one way." Andy Gill of The Independent found its "patina and keyboard tones" "blander" than Fur and Gold's music and said that it is difficult to "take Khan's stories seriously when she slips into blather about 'a stranger in a strange land' and 'a vast and unknowable universe'."Robert Christgau of MSN Music found her "as ill-informed about astronomy as she is about love" and panned her lyrics as "ill-informed mentions of goodbye beds and licking her clean."
Slant Magazine placed the album at number ninety-seven on its list of the best albums of the 2000s decade.