The station opened on 2 October 1900 as a branch of Line 1 from Étoile to Trocadéro. On 5 November 1903 this line was extended to Passy and the line from Étoile to Trocadéro and Passy became known as Line 2 South as part of a planned ring line around central Paris to be built under or over the boulevards built in place of the demolished Wall of the Farmers-General; this circle is now operated as two lines: 2 and 6. On 14 October 1907 the line from Étoile to Trocadéro, Place d'Italie and Gare du Nord became part of Line 5. On 6 October 1942 the section of Line 5 from Étoile to Place d'Italie, including Boissière, was transferred to Line 6. The Avenue Kléber commemorates Jean Baptiste Kléber (1753–1800), a General in the Revolutionary and Napoleonic Wars, and particularly noted for his leadership in the Egyptian campaign, where he was assassinated.
Although Charles de Gaulle - Étoile is designated as the terminus of Line 6, the single track loop at Charles de Gaulle - Étoile limits the capacity of Line 6 at that station. Instead of having an extended terminal stop at Charles de Gaulle - Étoile, Line 6 trains depart quickly back round the loop and then stop for an extended period of time at Kléber, which has extra platforms and tracks to accommodate the arrangement.