TOKYO—Toshiba Corp. seemed poised to profit from a global nuclear power revival when it paid $5.4 billion to win a bidding war for Westinghouse Electric Co. in 2006.

Today, that bet threatens to sink the venerable Japanese conglomerate, as cost overruns and missed deadlines on nuclear reactor projects around the world have forced it to warn investors that it may soon have to report billions of dollars in losses.

Toshiba...