The former presidential candidate is the former CEO of technology company Hewlett-Packard.
Mrs Fiorina dropped out of the presidential race after a poor showing at the New Hampshire primary.
She has been an active supporter for Mr Cruz, a senator from Texas, on the campaign trail.
The early announcement is unusual because vice-presidential picks are not normally decided until after a candidate secures the nomination.
"Over and over again, Carly has shattered glass ceilings," Mr Cruz said.
He doesn't have the Republican nomination. He doesn't even have the lead for the nomination. In fact, he has no clear path to the nomination. But it looks like Ted Cruz will have a running mate.
Naming Carly Fiorina as his vice-presidential pick at this point provides Mr Cruz with several benefits. First, he can generate some positive press and at least partially move on from the drubbing he received at the hands of Donald Trump in Tuesday's mid-Atlantic primaries.
Second, he positions his campaign to make a strong play for that grand prize on the horizon, the California primary on 7 June - a battleground that could decide whether Mr Trump secures the Republican nomination without a convention fight.
While Mrs Fiorina's 2010 general-election bid for a Senate seat there was spectacularly unsuccessful, she did win her party's nomination and is a known quantity among the state's conservative voters.
Mr Cruz has his back to the wall. He needs a win in Indiana, and he really needs a strong performance in California. Mrs Fiorina on the ticket could help - and at this point, anything that might work is worth a shot.
Mrs Fiorina could help Mr Cruz in his battle against front-runner Donald Trump, who has made disparaging comments about women - including her.
"Look at that face. Would anyone vote for that? Can you imagine that, the face of our next president?" he said.
Mrs Fiorina responded: "I think women all over this country heard very clearly what Mr Trump said."
Mr Cruz alluded to this exchange in introducing Mrs Fiorina in Indiana, saying she handled it with "grace and class".
While at Hewlett-Packard, Mrs Fiorina laid off 30,000 people and was fired by the company's board, though she has argued that her leadership "saved" the company.
She also had a failed bid for a California Senate seat.
Donald Trump's son Eric Trump called the move desperate.
While addressing the crowd, Mrs Fiorina broke into song.
She sang about Mr Cruz's daughters and their times together on the Cruz campaign bus.
"Donald Trump and Hillary Clinton are two sides of the same coin," she said, and Mr Cruz's presidential bid is not over yet, despite what "the media says".

The tie-up could worsen the position for shoppers in local areas owing to a cut in quality, fewer promotions and store closures, an initial probe found.
Poundland wants to buy its closest rival in an agreed deal worth £47.5m in cash and £7.5m in shares.
The Competition and Markets Authority (CMA) said this could hit 80 areas.
These were where the companies, which have a combined network of 800 stores, currently overlap. There was a further 12 areas where they would be competitors in the near future.
Following an initial investigation, the CMA said there was "a realistic prospect of substantial lessening of competition" in these areas.
The authority said it would now move to a more in-depth investigation unless these concerns were addressed in a "clear-cut manner" by the companies.
Republican presidential candidate Ted Cruz has announced Carly Fiorina as his running mate, calling her a "consistent, courageous fighter".
[NEXT_CONCEPT]
Discount store Poundland's proposed purchase of rival 99p Stores for £55m faces an in-depth investigation by competition authorities.