Dons top scorer Vernon, with nine goals to his credit this season, has put pen to paper in a deal that sees him remain with the club until the summer of 2014.
Meanwhile Considine, a product of the Pittodrie youth system, has signed until the summer of 2015.
Vernon, 28, joined Aberdeen from Colchester in the summer of 2010 and has previously played for Blackpool, Southed United, Oldham, Gillingham and Northampton while 24-year-old Considine made his debut as a teenager in season 2003-4.
Dons boss Craig Brown said: "Both Scott and Andy are integral to my plans here at the Club and I'm naturally very pleased they have pledged their futures here.
"I have already gone on record that I believe Scott can reach the twenty goal tally this season while Andy is the most improved player in our squad this season and one of the first names on the team-sheet each week."