Mayor Bloomberg is set to announce tomorrow that Cornell University has won the bid to construct a massive new science and engineering campus on Roosevelt Island, sources told The Post.

The upstate Ivy League school had been expected to claim the prize after its main rival, Stanford University, suddenly withdrew Friday.

Cornell also announced Friday that it had received an anonymous $350-million gift towards the state-of-the-art campus.

The Ithaca-based school, which also had outbid Stanford, was willing to spend more to help pay for the toxic cleanup required at the Roosevelt Island site, the sources said.

The new campus will spread Cornell’s presence in the Big Apple, as its medical school is right across the river from the proposed new site.

Besides getting the city-owned land to build the campus, Cornell is also set to collect $100 million in city-financed projects.

The nationwide search for top-tier colleges to build a new site was announced in July. It also drew interest from Columbia, NYU, Carnegie Mellon and Purdue University.