The trade became official on Sunday, with the Leafs sending goalie Ben Scrivens, forward Matt Frattin and a second-round draft pick to the Los Angeles Kings.
"I'm very happy," Bernier told the Los Angeles Times. "And [Maple Leaf Sports & Entertainment President and CEO] Tim [Leiweke] just called. He's very excited to have me on board."
Bernier, 24, is set to become a restricted free agent after making $1.525 million US last season. Nonis said no contract talks have taken place between the Leafs and their new netminder, but he doesn't anticipate a problem in getting a deal done.
The GM also said that in no way should the trade be looked upon as a vote of non-confidence for James Reimer.
"It's not a knock on James at all," Nonis said in a conference call. "I don't think you can be deep enough at that position.
"We feel we've got two of the top young goaltenders in the league right now. . . I'm looking forward to getting them both together. I think it's going to be a good fit."
Nonis said he had not spoken yet with Reimer but had left a message for him and expected they would talk soon.
Bernier was the backup behind 2012 playoff MVP Jonathan Quick, meaning playing time in Los Angeles was scarce. He played in only 14 games in 2013, posting a record of 9-3-1 with a 1.88 goals-against average and a .922 save percentage.
His desire for more playing time led to the Kings deciding to move him. Nonis confirmed the Leafs were a contender for his services right from the start of the regular season.
"It's kind of bittersweet for us, Jon's been with us a long time. He's been a great soldier for us and he's been a very good player for us," Kings assistant GM Ron Hextall told the team's official website.
"Unfortunately, he's stuck behind Jonathan Quick which is a tough situation for Jon, and as a sense of fairness to him and at the timing that we felt was the best for the organization, we made the move."
Nonis said both goalies will be given the opportunity to earn the starter's job in Toronto.
"Nothing's being guaranteed to anybody," he said. "When you have someone pushing you, you get the most out of yourself."
He also reiterated earlier remarks that the Leafs may continue to deal in order to upgrade at every position.
New King 'excited'
The 25-year-old Frattin played 82 games with the Leafs over parts of three seasons. He scored seven goals and 13 points in 25 regular-season games in 2013, adding two assists in six playoff contests.
"Just want to thank @MapleLeafs for a first class experience to start my pro career" Frattin tweeted. "Very excited to join @LAKings."
Scrivens, 26, played 32 games in a Leafs uniform over the last two seasons. He saw action in 20 games in 2013, accumulating a 7-9-0 record with a 2.69 GAA and a .915 save percentage.
The second-round draft pick sent to L.A. in the deal will be used in either 2014 or 2015. Toronto can choose which year they will defer the pick, and Nonis said the Leafs can hold off on that decision right up until the second round of the 2014 draft.