The Italienische SS-Freiwilligen-Legion (also known as the Legione SS Italiana) was formed in March 1944 from Italian volunteers in SS-Ausbildungsstab Italien under SS-Brigadeführer Peter Hansen. A total of 29 recruiting centers were formed in the German controlled areas of Italy by an order dated 18 February 1944.
Two battalions from the Legion were sent to the Anzio front in April, the Vendetta battalion (II. Bataillon, 81. Waffen-Grenadier-Regiment der SS) commanded by Waffen-Obersturmbannführer Frederico degli Oddi and the Debica battalion (Füsilier-Battailon 29) commanded by Waffen-Sturmbannführer Sassi, and were attached to the Reichsführer-SS division. After the fighting at Anzio these two battalions would serve with SS-Kampfgruppe Binz until the end of the war.
On 3 May 1944 Heinrich Himmler issued the below proclamation about the two battalions:

Because of the demonstration of courage and sense of duty displayed by the volunteers of the Italian SS, they are designated as units of the Waffen-SS with all of the duties and rights that that implies. (1)

It was redesignated 1. Sturmbrigade Italienische Freiwilligen Legion in June.

Commanders

SS-Obergruppenführer Karl Wolff (? Mar 1944 - ? June 1944)

Footnotes

1. "Italian volunteers of the Waffen-SS" by Richard Landwerhr, page 13. It should be noted that this only applies to those two battalions, not the rest of the legion.

Sources used

Christopher Ailsby - Hitler's Renegades: Foreign nationals in the service of the Third Reich
Richard Landwehr - Italian Volunteers of the Waffen-SS
Hugh Page Taylor - Recruiting offices of the Italian SS in Italy (in The Military Advisor Vol 23, No 2)
Frank Thayer & Marco Pennisi - The insignia & organization of the Italian volunteers to the Waffen-SS (in The Military Advisor, Vol 7 No 4)

Reference material on this unit

Sergio Corbatti & Marco Nava - Sentire - Pensare - Volere: Storia della Legione SS italiana
Richard Landwehr - Italian Volunteers of the Waffen-SS