Standard Model Higgs boson searches at the Tevatron

We give an overview of Standard Model Higgs boson studies performed at the CDF and Dzero experiments at the Tevatron proton-antiproton collider. Combining the results of many individual analyses, most of which use the full data set available, an excess with a significance of 3.0 standard deviations with respect to the Standard Model hypothesis is observed at a Higgs boson mass of 125 GeV/$c^2$. At that mass, the combined best-fit cross section is consistent with the Standard Model prediction. Constraints are also placed on the Higgs boson couplings with fermions and electroweak vector bosons and are consistent with the Standard Model predictions within the uncertainties.