Johnson, a promising defenseman with the University of Michigan and taken with the number three overall pick in last year's draft, was dealt to the Kings after twice rejecting contract offers by the Hurricanes.
"We felt the opportunity to acquire Jack Johnson was something we couldn't pass up as we continue to search for ways to upgrade this franchise," Kings general manager Dean Lombardi said on the team's Web site.
"This move required that we give up two good players, but has the potential to help us in the near future as well as for many years to come."
In exchange for Johnson and Tverdovsky the Hurricanes get two players expected to step into starting roles as Carolina prepares to open the defence of their Stanley Cup title.
Gleason, a 23-year-old defenseman and former first round selection, had two goals and 19 assists in 78 games with the Kings last season while Belanger, a rugged forward, set career highs with 17 goals and 20 assists.
Tverdovsky, the second overall pick in the 1994 draft, joins his sixth team in 12 seasons and scored three goals with 20 assists in Carolina's run to the Stanley Cup.