The plan will need the approval of the NHL's Board of Governors, which will meet Wednesday in Las Vegas in advance of the NHL's annual awards ceremony, but that approval is considered a formality.
"I've said all along that as much as there's excitement for the shootout, I'd like to see the games decided before the shootout if possible, and this increases the probability,"Columbus Blue Jackets general manager Jarmo Kekalainen told ESPN.com after the GMs' meeting broke Tuesday afternoon.
"If it gets approved by the Board of Governors tomorrow I think it's a good change and we've seen evidence of a lot more games decided in the overtime with that change both in the American [Hockey] League and the Swedish league," Kekalainen added.
The NHL had entertained the idea of a hybrid overtime that would have started with 4-on-4 and then gone to 3-on-3 for the final three minutes of overtime.
But the players' union was reluctant to endorse additional time to games, suggesting the game's top players would be adversely impacted as they are the ones who generally play the most in the overtime sessions.
The shootout was introduced after the 2004-05 lockout as a measure of ensuring each game had a winner and to add an exciting wrinkle after the labor stoppage that scuttled an entire season.
But over time, GMs have become increasingly frustrated at the number of games that were decided by the shootout as they felt important points in the standings were being decided essentially by a skills competition.
There were 170 shootouts last season representing 13.8 percent of all games. The year before, there were 178 or 14.5 percent of all games.
"I think what the goal was here was to reduce the shootouts," Nashville GM David Poile said Tuesday.
"The managers just really felt they'd like to end more games in an overtime situation versus the shootout," Poile said.
If the rule change is adopted, "I think it's going to be unbelievably exciting and I think we're going to get a lot of games that re going to be ended in overtime so I think we're going to get our wish," the Nashville GM added.
Former NHL goaltender Ron Hextall, now the general manager of the Philadelphia Flyers, said the 3-on-3 play won't be much fun for goaltenders given the scoring chances that are bound to be created by having so much open ice. But he believes the change is much needed.
"I think there's too many shootouts and the 3-on-3s, as much as the fans like the shootouts, they're really going to like the 3-on-3," Hextall said.
"I saw a lot of it at the American [Hockey] League level," he added. "It's exciting. It's free-flowing. It's chance-for-chance. It's tough on a goalie but it's exciting."
NHL opts for 3-on-3 overtime
Scott Burnside and Craig Custance break down the NHL owners' voting to move overtime to five minutes long with three skaters to a side.