Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a 1-to-1 correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson's axioms and Ξ : GrΛ → Sym • OX G is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on G and Σ is a class in F 1 H 2 (L, C), the first Hodge filtration piece of the second cohomology of L.As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.