Stenhammar was born in Stockholm, where he received his first musical education. He then went to Berlin to further his studies in music. He became a glowing admirer of German music, particularly that of Richard Wagner and Anton Bruckner. Stenhammar himself described the style of his First Symphony in F major as "idyllic Bruckner". He subsequently sought to emancipate himself and write in a more "Nordic" style, looking to Carl Nielsen and Jean Sibelius for guidance. The latter's Symphony No. 2, especially, had a great effect on him, leading him to change his style and refuse to refer to his First Symphony as anything but a trivial piece.
From 1906 to 1922 he was Artistic Director and chief conductor of the Gothenburg Symphony, the first full-time professional orchestra in Sweden. In this capacity, he organised many performances of music by contemporary Scandinavian composers. In 1909, he briefly held the position of director of music at Uppsala University, where he was succeeded the following year by Hugo Alfvén.
His works were quite varied and included two completed symphonies, a substantial Serenade for Orchestra, two piano concertos, four piano sonatas, a violin sonata, six string quartets, many songs and other vocal works, including several large-scale works for chorus or voices and orchestra: the early ballad "Florez och Blanzeflor" op. 3 written around 1891, "Ithaka" op. 21 from 1904, the cantatas Ett folk (A people) from 1905 and Sången (The song) op. 44 from 1921.
Writing in The Chamber Music Journal, R.H.R. Silvertrust notes that Stenhammar's six string quartets are the most important written between those of Brahms and Bartok. Whether or not this is so, there is no denying that Stenhammar's quartets represent a very important development during the twenty-five years he was writing chamber music. Tonally, they range from the middle late Romantics to a style akin to mature Sibelius. Though not unknown by the Swedish chamber music public, his string quartets have been sadly neglected elsewhere. In 2008 Musikaliska konstföreningen published the world premiere edition of his Allegro Brillante for piano quartet composed in 1891 and his Allegro non tanto for piano trio composed in 1895.
Stenhammar was considered the finest Swedish pianist of his time. Concert pianists who venture into the realm of the string quartet often wind up writing compositions which sound as though they were composed at, and are perhaps better played on, the piano. That Stenhammar's works show no such trait is because for nearly half of his life, he worked intimately with the Aulin Quartet, the top Swedish string quartet of his day and one of the best then performing in Europe. In fact, he toured throughout Europe with them for many years and a piano quintet was nearly always featured on their programmes. Thus it is no accident that his quartets show a fine grasp of instrumental timbre and technique. The part writing is sure, always idiomatic and evenly distributed.
List of compositions 
- Orchestral works
- Piano Concerto No. 1 in B-flat minor, Opus 1 (1893)
- Excelsior! Concert Overture, Opus 13 (1896)
- Symphony No. 1 in F major (1902–03, withdrawn)
- Piano Concerto No. 2 in D minor, Opus 23 (1904–1907)
- Two Sentimental Romances for violin and orchestra, Opus 28 (1910)
- Serenade in F major, Opus 31 (1908–13, rev.1919)
- Symphony No. 2 in G minor, Opus 34 (1911–1915)
- Symphony No. 3 in C major (1918–19, fragment)
- Opera and choral works
- Florez and Blanzeflor (for baritone and orchestra), Opus 3 (1891)
- Gildet på Solhaug (opera), Opus 6 (1892–1893)
- “Tirfing” (opera), Opus 15 (1897–1898)
- Ithaka (for baritone and orchestra), Opus 21 (1904)
- Ett Folk (cantata), Opus 22 (1904–1905)
- Midvinter (for mixed chorus and orchestra), Opus 24 (1907)
- Sången (symphonic cantata for soloists, mixed chorus, children's choir and orchestra), Opus 44 (1921)
- Around 60 songs
- Chamber music
- String Quartet No. 1 in C major, Opus 2 (1894)
- String Quartet No. 2 in C minor, Opus 14 (1896)
- String Quartet No. 3 in F major, Opus 18 (1897–1900)
- String Quartet No. 4 in A minor, Opus 25 (1904–1909)
- String Quartet No. 5 in C major, Opus 29 (1910)
- String Quartet No. 6 in D minor, Opus 35 (1916)
- Violin Sonata in A minor, Opus 19 (1899–1900)
- Allegro ma non tanto in A Major, for Piano Trio (1895)
- Allegro Brillante in E flat Major, for Piano Quartet (1891)
- Piano music
- Sonata No. 1 in C major (1880)
- Sonata No. 2 in C minor (1881)
- Sonata No. 3 in A-flat major (1885)
- Sonata No. 4 in G minor (1890)
- Three Fantasies, Opus 11 (1895)
- Sonata in A-flat major, Opus 12 (1895)
- Late Summer - 5 piano pieces, Opus 33 (1914)
- "Programme Notes Archive: Stenhammar, Symphony 2". Norfolk Symphony Orchestra. Retrieved 2007-08-14.
- The Chamber Music Journal (1994), V (2): 1,4. Riverwoods, IL: Cobbett Association. ISSN 1535-1726.
- Some information in the above article appears on the website of Edition Silvertrust. Permission to use, copy, alter and distribute has been given to Wikipedia under the GNU License and GFDL.
- Wilhelm Stenhammar Complete String Quartets (Nos.1-6), Violin Sonata Op.19 & Allegro Brillante for Piano Quartet Soundbites & Information
- Biography on the site of the Swedish Music Information Centre
- Listen to Tre Körvisor - free MP3 recordings of : September, I Seraillets Have och Havde jeg en Dattersøn with Umeå Akademiska Kör.
- Listen to a free MP3 recording of Vårnatt with Hemavans Sommarkör 2006.
- Free scores by Stenhammar at the International Music Score Library Project