The album took two and a half years to make. It was primarily recorded at Whitfield Street Recording Studios in London, apart from piano parts, which were recorded at London's Westside Studios. The material was mastered at Sony Music Studios in New York. Contrarily to Basia's previous albums, The Sweetest Illusion moves away from electronically generated music towards traditional live instruments. Basia dedicated this album "to her family and compatriots in Poland as well as those scattered around the world". Two songs on the album incorporate Polish language: in "An Olive Tree" Basia sings: "Oliwkowe drzewo może spełnić twe marzenia" (English: "An olive tree can make your dreams come true") and towards the end of "Yearning", she sings the opening line from a Polish folk song: "Szła dzieweczka do laseczka, do zielonego". The latter was described by Basia as the song she is most proud of and the best she has ever written. Its lyrics are about "missing home" and to emphasize this feeling, the track includes whale vocalization, which was Danny's idea.
"More Fire Than Flame" was released as Japan-only single in 1993. In mid-April 1994, the ballad "Yearning" was serviced to contemporary jazz stations as the first US single, although in other territories it was released as the album's final single in late 1994. The track was accompanied by a music video directed by Howard Greenhalgh, in which Basia and her two nieces appeared in Polish folk costumes. The song failed to chart, but entered the Tokio Hot 100 list on Japanese radio station J-Wave. "Drunk on Love" was released as the next single in June 1994 and topped Billboard's Dance Club Songs. It was followed by "Third Time Lucky" later in 1994.
The album was met with particular commercial success in Japan where it became Basia's biggest-selling album and her only platinum record there. In the USA though, The Sweetest Illusion did not repeat the success of the two previous albums, nonetheless, it was certified gold by the Recording Industry Association of America in December 1994 for sales in excess of 500,000 units. It was her final major-label full-length studio album. In 2016, the album was re-released by independent UK label Cherry Red Records as 3 CD deluxe edition featuring instrumental versions and remixes.