In this paper a new consensus based algorithm for decentralized recursive estimation of parameters in linear discrete-time stochastic errors-in-variables MIMO systems is proposed. One starts from a multi-agent setting, in which an agent has access only to a subset of noisy input-output variables. The proposed algorithm consists of two stages. The first stage is based on a combination of local stochastic approximation algorithms for estimating input-output covariance functions based on locally available measurements and a dynamic first order consensus scheme. At the second stage each agent utilizes a stochastic approximation algorithm with expanding truncations for generating all system parameter estimates on the basis of current estimates of the matrices in the modified Yule-Walker equations obtained at the first stage. In the given convergence analysis it is proved that the estimates of the covariance functions and the overall parameter estimates converge almost surely to their true values under appropriate assumptions concerning system properties and the multi-agent network topology.