The 21-year-old moved to Gresty Road from non-league Lincoln City this summer, where he scored 13 goals in 41 games last season.
Oliver has revealed that he is relishing the opportunity to test himself in League One.
"I know I've come here to improve as a player and I know I will have to adapt to a different level of football having come from Lincoln and the Conference," he told Crewe's official website.
"I am determined to show that can handle the step up and can't wait to get going.
"It will be a great test for us all in League One but one we are all looking forward to. I am ready, prepared to muck in for the team and hopefully I can score goals to help the team."
Crewe begin the new season at home to Rotherham United on August 3.