Nils Paul "Palle" Danielsson was born October 15, 1946, in Bromma, a district of Stockholm, into a musical family — his sister, Monica Dominique, became a well-known pianist and composer in her own right. His start was unusually early even by prodigy standards: harmonica at two, violin at eight, and by his early teens a growing fascination with jazz that pulled him toward the double bass instead. He was already gigging professionally by fifteen, cutting his teeth at Stockholm's famed Gyllene Cirkeln (Golden Circle) jazz club, where the house rhythm section backed touring American stars passing through Sweden. In 1965, at nineteen, one of those American visitors was Bill Evans — an early credit Danielsson carried for the rest of his career. He also backed or recorded with Ben Webster, Svend Asmussen, and Steve Kuhn's trio in these same Stockholm years, and appears alongside Lee Konitz, Pony Poindexter, Phil Woods, and Leo Wright on the 1968 MPS session Alto Summit. In parallel with the club work, he pursued formal violin training at Stockholm's Royal Academy of Music from 1962 to 1966, so for several years he was simultaneously a conservatory string student and a working jazz bassist.

By 1973 Danielsson was a fixture of Sweden's new-jazz scene on two fronts at once: he co-founded the all-Swedish quartet Rena Rama with saxophonist Lennart Åberg, pianist Bobo Stenson, and drummer Bengt Berger, and in the same year began recording as the rhythm-section partner of the Jan Garbarek–Bobo Stenson Quartet, alongside drummer Jon Christensen. That group's 1974 ECM album Witchi-Tai-To is generally credited with widening Danielsson's reputation beyond Sweden — the record that put him in the orbit of ECM founder Manfred Eicher and, through Eicher, of Keith Jarrett, who was assembling a new group of his own that year.

The result was Jarrett's "European Quartet" (also called the "Belonging Quartet" after its first studio album), pairing the pianist with Garbarek, Danielsson, and Christensen from 1974 to 1979. Belonging (1974) and My Song (1978) are the quartet's two ECM studio albums; Nude Ants (recorded live at the Village Vanguard in May 1979, released 1981) and the archival releases Personal Mountains (recorded 1979, released 1989) and Sleeper (recorded in Tokyo on April 16, 1979, released 2012) filled out the group's live legacy long after it disbanded. Danielsson and Christensen also stayed on with Garbarek and Stenson for a second ECM date, Dansere (1976). Across the same mid-to-late-1970s stretch he became one of ECM's most in-demand session bassists more broadly, appearing on Enrico Rava's The Pilgrim and the Stars (1975) and The Plot (1977) with John Abercrombie and Christensen, Edward Vesala's Satu (1977), Collin Walcott's Grazing Dreams (1977) alongside Don Cherry, and the German-label date The Wide Point (MPS, 1975) with trombonist Albert Mangelsdorff and drummer Elvin Jones.

After the Jarrett quartet disbanded in 1979, Danielsson kept working at the center of European jazz rather than stepping into the spotlight himself. He toured and recorded with Carla Bley, with Charles Lloyd's quartet (the ECM album Fish Out of Water, 1990), and with pianist Michel Petrucciani. His longest-running post-Jarrett association was with drummer Peter Erskine's trio alongside British pianist John Taylor, a partnership that produced four ECM studio albums between 1993 and 1999 — You Never Know (1993), Time Being (1994), As It Is (1996), and Juni (1999) — and continued, after Erskine's departure, as the "John Taylor Trio" with drummer Martin France on Angel of the Presence (2006), Whirlpool (2007), and Giulia's Thursdays (2012). A ninth Taylor/Danielsson/France session recorded in Ludwigsburg in October 2006 was shelved for nearly two decades and finally released as Close to Mars in 2025, a year after Danielsson's own death and ten years after Taylor's.

Danielsson also built a substantial catalog beyond the ECM mainstream: Anouar Brahem's Khomsa (1995), Dino Saluzzi's Responsorium (2003), and two Swedish-folk-jazz crossover albums with fiddler/multi-instrumentalist duo Lena Willemark and Ale Möller, Nordan (1994) and Agram (1996). As a leader in his own right he moved slowly and rarely: his debut, Contra Post (1994, Caprice Records), paired him with pianist Rita Marcotulli, saxophonist Joakim Milder, and drummer Anders Kjellberg. Later co-led sessions included Traction Avant (1994, with pianist Alessandro Galati and Erskine), The Second Time Around (2013, with pianist Anders Persson and drummer Terje Sundby), Trio M/E/D (2015, reuniting Marcotulli with Erskine), and Togetherness (2012), a duo album with his sister Monica Dominique.

Danielsson received the Swedish Jazz Association's Lifetime Achievement Award in 2023, along with the Monica Zetterlund Scholarship and the Jan Johansson Scholarship earlier in his career. He died on May 18, 2024, at his home in Åkers Styckebruk, Sweden, after a period of illness, at age 77; he was survived by his sister Monica Dominique and his longtime partner, artist Ulla Lööf. Announcing his death, Dominique said, "I don't think everyone really understands how famous he was internationally," calling him "a highly respected and extremely knowledgeable fellow musician."

ECM's own house description of Danielsson calls him "a melodically imaginative, warm-toned bassist, with a great sense of drive" — a player who built a sixty-year career almost entirely as an ensemble anchor rather than a frontman, and who was valued precisely for that restraint. Manfred Eicher, who produced or oversaw most of his classic ECM sessions, credited him with "a very special sense of soulfulness and precision" and a "determination to serve the whole band sound" over his own visibility. Pianist Gareth Williams, reflecting on his death, called Danielsson's tone "one of the most instantly identifiable bass sounds of all time": deep, resonant, and endlessly warm — the sound that helped define the lyrical, spacious "ECM aesthetic" of the 1970s and that Danielsson carried, largely unchanged in character, through five subsequent decades of European and Scandinavian jazz.