The move follows the death of 13-year-old Brittanie Cecil, who was struck by a puck shot into the crowd at Nationwide Arena in Columbus on March 16.
"In response to the Brittanie Cecil tragedy, the National Hockey League has spent the past several months in comprehensive study of the arena and spectator environment at our games," Bettman said. "While the analysis confirmed that our arenas are safe, the determination was made to take additional measures that would reduce the incidence of pucks entering the stands."
The average height of the netting is expected to be 18 feet.
Bettman also mandated that protective glass along the sides of rinks extend at least five feet above the top of the boards.
The NHL Board of Governors, meanwhile, approved a new procedure designed to speed up line changes and faceoffs.
Under the new guidelines, the puck will be dropped within 20 seconds of a stoppage in play, except in the final two minutes of the third period or overtime and after goals are scored. The procedure is similar to one that proved popular at the Salt Lake City Olympics.
In the NHL, the visiting team will have five seconds and the home team eight seconds to make a line change. The linesman will blow his whistle and drop the puck five seconds after that.
If the center is not at the faceoff dot within the allotted five seconds, the puck will be dropped anyway.
Similar procedures were instituted this season in both the American Hockey League and Ontario Hockey League. In the AHL, the time of an average game was reduced 14 minutes.
In other action, the board agreed to impose a minor penalty on any player who disputes or argues with an official over a penalty assessed to a teammate. Previously, the punishment was a 10-minute misconduct. Players who persist in arguing a call, however, will receive a misconduct in addition to the minor penalty under the new rule.