In this paper, the performance of underlay cognitive dual-hop decode-and-forward (DF) multi-relay networks with best relay selection (BRS) over independent identically distributed (i.i.d.) Weibull fading channels is evaluated. The maximum transmit power of the secondary network is governed by the maximum interference power that the primary networks' receiver can tolerate. Specifically the closed-form outage probability (OP) with interference power constraints from the primary network is derived, using the statistical characteristics of the end-to-end signal-to-noise ratio (SNR). The analytical results have been verified by Monte-Carlo simulations