Fiorina, 61, dropped her own White House bid in February after a lackluster seventh-place finish in New Hampshire's first-in-the-nation primary. She endorsed Cruz, a 45-year-old U.S. senator from Texas, a month later and has been a sharp critic on the campaign trail of likely Democratic nominee Hillary Clinton.
Cruz's unusually early announcement of a running mate appeared to be a bid to recover from Tuesday's losses, which moved Trump closer to the 1,237 delegates he needs to win the nomination at the July 18-21 Republican convention in Cleveland. The nominee will face the Democrats' pick in November's general election.
Traditionally, the winners of the Republican and Democratic presidential races announce their running mates in the period between clinching the nomination and the summer national conventions.
But Cruz needs help after Tuesday's drubbing by Trump, 69, in all five Northeastern states that held primary elections: Pennsylvania, Maryland, Delaware, Connecticut and Rhode Island.
The choice of Fiorina, a former Hewlett-Packard chief executive who, like Trump, has never held elective office, could help Cruz with women voters, a group that Trump has had difficulty winning over to his outsider campaign.
It also could offer Cruz a boost in the June 7 primary in California, where in 2010 Fiorina won the Republican primary for the U.S. Senate. She was defeated in the subsequent general election by incumbent Democrat Barbara Boxer.