Wirén was born at Striberg near Nora. His father had a roller blind factory, and there were various musical activities in the family home; he took piano lessons, and was a student at the Karolinska school in Örebro, and played the bass drum and celesta in the town orchestra. 
Wirén studied at the Stockholm conservatory from 1926 to 1931, which gave him much exposure to music from all periods; hearing Arthur Honegger's oratorio King David in 1927 was an important experience.
In 1932 he won the state stipend and used the award money to continue his studies in Paris, where he lived from 1931 to 1934. While there, he studied composition under the Russian composer Leonid Sabaneyev, though he admitted later that his endless attendance of concerts, and not his tutoring with Sabaneyev, had the greater impact on his own work. In Paris he met Igor Stravinsky (as well as his compatriot Gösta Nystroem) and was exposed to the music of Stravinsky, Sergei Prokofiev and the French composers of Les Six.
In 1934, Wirén moved to Stockholm with his bride, the Irish cellist, Noel Franks, whom he had met in Paris; their daughter, Annika, was born in 1947. In 1937, the couple set up home permanently in Danderyd, just north of Stockholm. As well as composing, Wirén regularly played his main instrument, the piano, on Swedish Radio during the 1930s; he also devoted himself to chamber music in the 1930s and 40s; although he conducted in a recording of his Sinfonietta, he hated conducting. He was music critic at the "Svenska Morgonbladet" from 1938 to 1946, and in 1947 became Vice-Chairman of the Society of Swedish Composers. From 1948, he spent summers on the island of Björkö, in Stockholm's archipelago. He served as a member of the board of directors of the Royal Swedish Opera from 1962 to 1971. His TV ballet Den elaka drottningen (The Evil Queen) won the 1960 Prix Italia. He also wrote the music for the Swedish entry for the 1965 Eurovision Song Contest, Annorstädes vals (Absent Friend), sung by Ingvar Wixell. He retired from composing in 1970, commenting, "One should stop in time, while one still has time to stop in time."
He died at Danderyd on 19 April 1986.
Wirén's output, which ranges from serious to popular, is notable for its quality rather than quantity, and a number of his works were refused opus numbers or withdrawn. He once commented that his first desire was to entertain and please, and compose listener-friendly 'modern' music. He was reluctant to write for the voice (in the 1965 Eurovision Song Contest entry, Alf Henrikson wrote the lyrics after Wirén had composed the music).
Neoclassical pieces from Wirén's early Parisian period, including the Piano Trio (1933) and the Sinfonietta (1933–34), are melodically and rhythmically entertaining.
Upon his return to Sweden, he composed his first two symphonies and his most famous work, the Serenade for Strings (1937); the spirit of this serenade may also be found in the finale of his second symphony (1939). Wirén went on to compose five symphonies, concertos and other orchestral works, including music for the stage and film scores, as well as instrumental and chamber music, including a series of string quartets.
His musical style on return from Paris remained broadly neoclassical; melodic, energetic and with high spirits. Towards the mid-1940s Wirén became more serious in style, perhaps under the influence of Jean Sibelius. Wirén also developed a personal technique, first used in the third string quartet (1941–45), of gradual motivic transformation, avoiding repetition (metamorphosis technique). He pursued this approach in his third symphony (1944), where the first motif in the first movement, based on a step-wise Dorian mode progression, is transformed during the movement and then echoed in the last three movements. Motivic tautness also characterizes the deeply expressive fourth symphony (1952), as well as his rather cooler later works, including the fifth symphony (1964) and fifth string quartet (1970).
- Symphony 1, Op. 3 (1932)
- Symphony 2, Op. 14 (1939)
- Symphony 3, Op. 20 (1943–44)
- Symphony 4, Op. 27 (1951–52)
- Symphony 5, Op. 38 (1964)
- Concert Overture 1, Op. 2 (1931)
- Concert Overture 2, Op. 16 (1940)
- Lustspelsuvertyr, Op. 21 (1945)
- Sinfonietta, Op. 7a (1933–34)
- Two orchestral pieces, Op. 7b (1934)
- Serenade for strings, Op. 11 (1937)
- Little Suite, Op. 17 (1941)
- Romantic suite, Op. 22 (1943, rev. 1961)
- Divertimento, Op. 29 (1954–57)
- Triptych for small orchestra, Op. 33 (1958)
- Music for strings, Op. 40 (1966)
- Cello Concerto, Op. 10 (1936)
- Violin Concerto, Op. 23 (1946)
- Piano Concerto, Op. 26 (1950)
- Concertino for flute and small orchestra, Op. 44 (1972)
- String Quartet 1
- String Quartet 2, Op. 9 (1935)
- String Quartet 3, Op. 18 (1941)
- String Quartet 4, Op. 28 (1952–53)
- String Quartet 5, Op. 41 (1970)
- Piano trio 1, Op. 6 (1933)
- Piano trio 2, Op. 36 (1961)
- Wind quintet, Op. 42 (1971)
- Quartet for flute, oboe, clarinet and cello, Op. 31 (1956)
- Sonatina for violin and piano, Op. 15 (1940)
- Sonatina for cello and piano 1, Op. 1 (1931)
- Sonatina for cello and piano 2, Op. 4 (1933)
- Miniature suite for cello and piano, Op. 8a (1934)
- Miniature suite for piano trio, Op. 8b (1934)
- Theme with variations for piano, Op. 5 (1933)
- Small ironic pieces for piano, Op. 19 (1942–45)
- Sonatina for piano, Op. 25 (1950)
- Improvisations for piano, Op. 35 (1959)
- Little serenade for guitar, Op. 39 (1964)
- Little suite for piano, Op. 43 (1971)
- Titania for women’s voices, words by Gustaf Fröding (1942)
- Three sea poems a capella, words by Karin Boye (1963)
- Livet och skrifterna ("En helig man"), words by Nils Ferlin (1934)
- Mitt trollslott står i skogens bryn, words by August Strindberg (1934)
- To your bed, Op. 13a, An autumn evening, Op. 13b, words by Erik Axel Karlfeldt (1938)
- Jungfru Maria and Malenavisorna, Op. 13 a-b (1938), words by Erik Axel Karlfeldt
- Annorstädes vals, words by Alf Henrikson (1965)
Works for the stage
- Ballet Oscarian ball, Op. 24, after Gustaf Fröding’s "Balen" (1948–49), (Royal Stockholm Opera, 1950, choreography by Birgit Cullberg)
- Radio operetta, Gult, rött och blått, libretto by Georg Eliasson (Swedish Radio, 1940)
- Radio operetta, Den glada patiencen, libretto by Georg Eliasson (Swedish Radio, 1941)
- Incidental music for Madame Bovary, (Gustave Flaubert), Blancheteatern 1939
- Stage music for Amorina (Carl Jonas Love Almqvist), Kungliga Dramatiska Teatern, 1951
- Music for The Merchant of Venice, William Shakespeare (1943), Kungliga Dramatiska Teatern
- Incidental music for Romeo and Juliet (William Shakespeare), Kungliga Dramatiska Teatern, 1953
- Stage music for Gudens hustru, (Vilhelm Moberg), Kungliga Dramatiska Teatern, 1954
- Music for A midsummer night’s dream, Kungliga Dramatiska Teatern, 1955
- Music for The Queen's Tiara (Carl Jonas Love Almqvist), Kungliga Dramatiska Teatern, 1957
- Ballet Take your place on stage
- Ballet, Den elaka drottningen, Sveriges Television 1960, choreography by Birgit Cullberg
- Stage music for Hamlet (Shakespeare), Kungliga Dramatiska Teatern, 1960
- Stage music for King John (Shakespeare), Kungliga Dramatiska Teatern, 1961
- Man glömmer ingenting (One Forgets Nothing) (1942)
- Oss tjuvar emellan eller En burk ananas (1945)
- Grönt guld (1949)
- Only a Mother (1949)
- Miss Julie (1951)
- A Lesson in Love (1954)
- Wild Birds (1955)
- The Phantom Carriage (1958)
- De sista stegen (A matter of morals) (1961)
As conductor Wirén recorded his Sinfonietta in May 1948 for Cupol, reissued on Phono Suecia PSCD 79, 1995.
- Dag Wirén Foundation website - biography.
- Cnattingius CM. Contemporary Swedish Music. The Swedish Institute, Stockholm, 1973.
- Jacobsson, Stig. Dag Wirén – life and works. CD notes for CPO 999 563-2, 1998.
- Åhlén C. G. Swedish composers conduct their own works 1937-1950. CD notes for Phono Suecia PSCD 79, 1995.
- Brandel Å. A Mature Generation: Larsson, Wirén, de Frumerie, Koch. In: Sweden in music. Musikrevy International, Stockholm, 1960.
- Haglund, Rolf. "Wirén, Dag". Grove Music Online. Oxford Music Online, Oxford University Press. Retrieved 17 September 2013.(subscription required)
- See Eurovision Song Contest 1965
- A list of Wirén autographs with some information about dates
- Broadcast from 1960 of Wirén's Violin Concerto Op. 23 (British Library)