Gregerson was named to the role over hard-throwing Ken Giles, who was acquired from the Phillies in a blockbuster trade this past offseason that sent 2013 top overall draft pick Mark Appel to Philadelphia.
Hinch made the announcement Monday after Houston's scheduled opener against the Yankees in New York was postponed a day because of wet and cold weather.
Gregerson, 31, had a career-high 31 saves in 36 chances and a 3.10 ERA as Houston's closer last season.
"He's got a slow heartbeat. He's got a real feel for how to pitch,'' Hinch said. "His calmness in the intense moments are critical in giving the guy the ball the last part of the game.''
Gregerson and Giles did not discuss the decision with reporters in the Astros clubhouse.
"Ken Giles will be used in a more versatile role,'' Hinch said. "The titles and the distinction and the status are secondary to the goal of the night, which is to win the game.''
Hinch did not rule out the possibility that the 25-year-old Giles, who had 15 saves in 17 chances and a 1.80 ERA in 2015 but struggled throughout spring training, could get some save opportunities.
"We've got a long career ahead of Ken Giles, so I think he can work his way into any role,'' Hinch said. "So where he starts on April 4 versus what out he gets on any given day throughout the season could change.''
The Associated Press contributed to this report.