Luck is widely considered to be the most polished college quarterback prospect since Peyton Manning, the four-time NFL Most Valuable Player he will replace in Indianapolis.
"In fairness to Andrew Luck and in fairness to the whole process - the media gauntlet he's going to be enduring the next couple days - I thought it was the right thing to do to announce that we are going to take him," Colts General Manager Ryan Grigson told reporters in a video posted on the team's website.
"Didn't see the point in prolonging what the world already knows pretty much."
The Colts gained the top draft pick in Thursday's opening round pick after compiling an NFL-worst 2-14 record last season as Manning missed the entire campaign following neck surgery.
With Luck available, Indianapolis decided not to exercise their option to bring back the 36-year-old Manning, who ended up signing a five-year, $96 million deal with the Denver Broncos.
Luck threw for 3,517 yards and 37 touchdowns with 10 interceptions in his final season at Stanford.
Baylor quarterback Robert Griffin III, who edged out Luck for the Heisman Trophy last December as the top U.S. collegiate player, is expected to be taken second overall by the Washington Redskins.
Following opening round selections at New York City's Radio City Music Hall, the NFL draft will resume Friday with rounds two and three and conclude Saturday with rounds four to seven.
Colts coach Chuck Pagano said the team was supremely confident in its choice of Luck.
"We did our due diligence, we studied him like heck and everybody thought this was the foregone conclusion," the coach said.
"The intangibles are off the chart. You know the skill set, you've seen the body of work. He's a gym rat, he's a football junkie, he's big, he's strong, he's physical. He can make every throw out there and he's a great leader in his own way."
After posting their dismal record in Manning's absence, the Colts decided it was time to rebuild, from the roster to the front office, and the team heads into the 2012 season with a new coach and general manager in addition to a new quarterback.
"We've got a great one for years to come and it's another piece of the puzzle that we feel really good about, obviously," said Pagano.
"I know this. On any level if you don't have a quarterback it's really, really hard to win. Especially in the NFL, so I am going to sleep well at night knowing we have a quarterback for a long time."