symmetric monoidal (∞,1)-category of spectra
the model structure for -module spectra;
and the model structure on chain complexes (unbounded).
This induces a Quillen equivalence between the corresponding model structures on monoids in these monoidal categories, which on the left is the model structure on -algebra spectra and on the right the model structure on dg-algebras:
This is due to (Shipley). The corresponding equivalence of (∞,1)-categories for a commutative rings with the intrinsically defined (∞,1)-category of E1-algebra objects on the left appears as (Lurie, prop. 188.8.131.52).
This is a stable version of the monoidal Dold-Kan correspondence. See there for more details.
An account in terms of (∞,1)-category theory is in section 7.1.4 of
The equivalence of -algebra spectra with dg-algebras is due to
Eilenberg-MacLane spectra for itself a dg-algebra are discussed in
See also the references at stable homotopy theory.