The new deals will see the pair remain at the club until 2020.
Recruited from GWS at the end of 2016, Stewart has played 23 games and kicked 37 goals for the Bombers.
Stewart told the Bombers’ official website he was looking forward to finishing off the year strongly in the Bombers VFL finals campaign.
“I’m excited to spend the next two years at Essendon. I believe this side is on the cusp of something special and I’m excited to see what we can achieve together as a team,” Stewart said.
“At the moment my focus is on the next couple of weeks and hopefully having some success with the VFL squad.
“This year hasn’t been ideal for me but I know that this journey and upcoming pre-season will set the foundation for 2019 and beyond.”
Laverde has played 30 games for the Bombers since being drafted with pick 20 in the 2014 NAB AFL Draft.
The 22-year-old said he was thrilled to extend his stay at the Bombers.
“The club has a bright future ahead and I’m looking forward to being a consistent contributor to the side over the next two years,” Laverde said.
“The team finished off the year strongly and we can all see the positive direction we are heading in.
“Over the next two years I want to develop my game and continue to build on the time I spend in the midfield.
“Right now, I can’t wait to continue with VFL finals and then plan to hit the ground running in the pre-season and advance my game as much as possible.”
Essendon’s VFL side will face the Casey Demons in the VFL Preliminary Final this weekend.