The Ducks announced the entry-level deal Saturday.
Drysdale was the second defenseman chosen in the draft last month. The 18-year-old prospect was a first-team All-Star in the Ontario Hockey League last season for the Erie Otters, collecting 47 points in 49 games.
Drysdale also has been invited to Team Canada's camp later this month for the 2021 World Junior Championship. The smooth two-way defenseman was a member of Canada's gold medal-winning World Junior Championship team earlier this year.