The 44-year-old Texan is to set out his plans in detail in a speech at Liberty University in Virginia on Monday.
In a video posted on Twitter, he says: “It is going to take a new generation of courageous conservatives to make America great again.”
Commentators say Mr Cruz, a Tea Party favourite, splits Republican opinion.
Several White House hopefuls are expected to announce their bids for the presidency in the coming weeks.
Mr Cruz may go up against the likes of Jeb Bush, an early Republican frontrunner, and New Jersey Governor Chris Christie, who are yet to formally declare their candidacy.
Republican Senators Rand Paul and Marco Rubio have also hinted at their own White House interests.
Meanwhile, Hillary Clinton is widely expected to be among those standing for the Democratic Party nomination.
Mr Cruz is a leading conservative who was elected to the US Senate in 2012.
In September 2013, the firebrand politician gave a 21-hour speech against President Barack Obama’s health law – one of the longest speeches in Senate history.
His eligibility to run for the White House was thrown into doubt after it emerged he was born in Canada, and he was forced to formally give up his dual citizenship last year.