Michael R. Bloomberg, who bypassed his own run for the presidency this election cycle, will endorse Hillary Clinton in a prime-time address at the Democratic convention and make the case for Mrs. Clinton as the best choice for moderate voters in 2016, an adviser to Mr. Bloomberg said.

The news is an unexpected move from Mr. Bloomberg, who has not been a member of the Democratic Party since 2000; was elected the mayor of New York City as a Republican; and later became an independent.

But it reflects Mr. Bloomberg’s increasing dismay about the rise of Donald J. Trump and a determination to see that the Republican nominee is defeated.