The event comes one day after Trump outlined his "America first" foreign policy in Washington.
But he said he would not be "a happy trigger," calling nuclear weapons "a horror."
The new VP pick bashed her opponents on both sides of the aisle.
The Texas senator had been teasing a "major announcement" all day.
The Susan B. Anthony List praised Fiorina ahead of the Cruz announcement.
Cruz has been teasing a major announcement for later Wednesday.
WH press secretary: "Apparently, the phonetics are not included on the teleprompter."
"The voters have spoken,” Rick Scott wrote on Facebook.
"Last night was Donald Trump's night, and today is Indiana's day," Cruz told reporters.
The speech comes one day after Trump swept five primaries in Northeast states.