WASHINGTON—Top state law-enforcement officials from across the country are formally launching antitrust probes into Facebook Inc. and Alphabet Inc.’s Google starting next week, further pressuring tech giants already under federal scrutiny over whether their online dominance stifles competition.

The moves, involving two large bipartisan coalitions of state attorneys general, add considerable heft to the investigative efforts under way in Washington. As in the government’s antitrust action against Microsoft Corp. two decades...