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Established in 1892, Bromley initially played in the South London League, before becoming a founder member of the Southern League in 1894, joining Division Two. However, after finishing bottom of Division Two in 1895–96 they left to become founder members of the London League, also joining Division Two. They won the division at the first attempt and were promoted to Division One. They switched to the Kent League for the 1898–99 season, but after finishing bottom of the league, they returned to Division One of the London League. During the 1899–1900 season, the club withdrew from Division One, taking over their reserves' fixtures in Division Two. They withdrew from Division Two at the end of the 1900–01 season.

In 1907 the club were founder members of the Spartan League and went on to become its inaugural champions. They joined the Isthmian League for the following season, and won back-to-back titles in 1908–09 and 1909–10. In 1910–11 the club won the FA Amateur Cup, beating Bishop Auckland 1–0 in the final. The season also saw them finish seventh in 1910–11, the club returned to the Kent League and were placed in Division One. They remained in the league until World War I, but joined the Athenian League when football resumed in 1919. The club were Athenian League champions in 1922–23. In 1937–38 they reached the first round of the FA Cup for the first time. After beating King's Lynn in the first round, they lost 4–1 at Scarborough in the second. They also reached the final of the FA Amateur Cup again, beating Erith & Belvedere 1–0. The club repeated the feat the following season, this time playing Football League opposition for the first time as they lost 8–1 at Lincoln City in the second round. In 1945–46 another second round appearance resulted in a 4–2 aggregate defeat to Watford. In 1947–48 they held Reading to a 1–1 draw in the first round, before losing the replay at Elm Park 3–0.

The club won another Athenian League title and the FA Amateur Cup in 1948–49, with the following season seeing another FA first round defeat, this time 2–1 to Watford. In 1950–51 the club won their third Athenian League title; the season also saw them lose 1–0 to Aldershot in the FA Cup first round. Going straight into the first round the following season, they lost 3–2 at Torquay United. In 1952 they rejoined the Isthmian League, and after finishing as runners-up in their first season back in the league, they were champions in 1953–54. They won the league for a fourth time in 1960–61.

After finishing bottom of Division One in the 1974–75 season Bromley were relegated to Division Two. In 1976–77 the club appeared in the FA Cup first round for the first time in over twenty years, losing 7–0 at Swindon Town. Division Two became Division One in 1977, and the club were promoted to the Premier Division after finishing as runners-up in 1979–80. They were relegated to Division One again in 1983–84, but returned to the Premier Division as Division One runners-up in 1985–86. Another relegation followed in 1989–90, but was followed by an immediate return to the Premier Division as Division One runners-up in 1990–91. In 1996–97 they qualified for the FA Cup first round again, but were beaten 3–1 at home by Enfield.

Bromley were relegated to Division One of the Isthmian League again at the end of the 1998–99 season; non-league reorganisation in 2004 saw Division One become the eighth rather than seventh tier of the football pyramid. A fourth-place finish that season saw them qualify for the promotion play-offs, and after defeating Metropolitan Police on penalties in the semi-finals, they beat Horsham 3–1 in the final to earn promotion to the Isthmian Premier Division. In 2006–07 they finished as runners-up in the Premier Division, again qualifying for the promotion play-offs. A 1–0 win over AFC Wimbledon in the semi-finals and a victory against Billericay Town on penalties in the final saw them promoted to the Conference South. The season had also seen them reach the FA Cup first round again, eventually losing 4–1 at Gillingham. Further appearances in the first round were achieved in 2009–10 (against Colchester United), 2011–12 (Leyton Orient), 2012–13 (Fleetwood Town) and 2014–15 (Dartford), but they were beaten on each occasion.

In 2014–15 Bromley won the Conference South, earning promotion to the renamed National League. Another FA Cup first round appearance in 2017–18 saw them defeated by Rochdale. The season also saw them reach the final of the FA Trophy, where they lost 5–4 on penalties to Brackley Town after the match had ended in a 1–1 draw. In 2020–21 the club finished seventh in the National League, qualifying for the promotion play-offs, in which they lost 3–2 to Hartlepool United in the quarter-finals. The club won the FA Trophy for the first time in their history in 2021–22, beating Wrexham 1–0 in the final. In the 2022–23 season they finished seventh in the National League again. In the play-offs the club defeated Woking 2–1 in the quarter-finals, before losing 3–2 to Chesterfield in the semi-finals. In the 2023–24 season, Bromley achieved promotion to League Two after defeating Solihull Moors 4–3 on penalties in the promotion play-off final, entering the Football League for the first time in the club's history.