This work is concerned with the consensus problem of multi-agent systems with additive and multiplicative measurement noises. By developing general stochastic stability lemmas for nonautonomous stochastic differential equations, stochastic weak and strong consensus conditions are investigated under fixed and time-varying topologies, respectively. For the case with fixed topologies and additive noises, the necessary and sufficient conditions for almost sure strong consensus are given. It is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs, and almost sure weak consensus implies mean square weak consensus under undirected graphs; if multiplicative noises appear, then small noise intensities do not affect the control gain to guarantee stochastic strong consensus. For the case with time-varying topologies, sufficient consensus conditions are given under the periodically connected condition of the topology flow.