Morris played 30 times for the Cod Army last season, scoring two goals.
“Shayden is an exciting young player, and we are delighted he has chosen Aberdeen as the next step to further his career,” said Aberdeen manager Jim Goodwin.
“He has a huge amount of potential, and his arrival aligns with the strategy here at the club to be the best developer of talent.
“Having watched him extensively he ticks a lot of boxes for us in terms of the speed he will bring to the team.
“We look forward to working with Shayden and I am confident he will thrive upon the demands here at Aberdeen.”