OLATHE, Kan.—The man who admitted killing three people at two suburban Kansas City Jewish sites gave jurors a Nazi salute Monday after they convicted him of murder and other charges for the shootings, which he said would allow him to “die a martyr.”

It took the jury of seven men and five women just over two hours to find Frazier Glenn Miller Jr. guilty of one count of capital murder, three counts of attempted murder and assault and weapons charges.

After...