Cosmological variation of the fine structure constant α due to the evolution of a spatially homogeneous ultra-light scalar field (m ∼ H_0) during the matter and Λ dominated eras is analyzed. Agreement of Δα/α with the value suggested by recent observations of quasar absorption lines is obtained by adjusting a single parameter, the coupling of the scalar field to matter. Asymptotically α(t) in this model goes to a constant value α̅≈α_0 in the early radiation and the late Λ dominated eras. The

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... pling of the scalar field to (nonrelativistic) matter drives α slightly away from α̅ in the epochs when the density of matter is important. Simultaneous agreement with the more restrictive bounds on the variation |Δα/α| from the Oklo natural fission reactor and from meteorite samples can be achieved if the mass of the scalar field is on the order of 0.5--0.6 H_Λ, where H_Λ = Ω_Λ^1/2 H_0. Depending on the scalar field mass, α may be slightly smaller or larger than α_0 at the times of big bang nucleosynthesis, the emission of the cosmic microwave background, the formation of early solar system meteorites, and the Oklo reactor. The effects on the evolution of α due to nonzero mass for the scalar field are emphasized. An order of magnitude improvement in the laboratory technique could lead to a detection of (α̇/α)_0.