With the two-week recruitment period drawing to a close, employers will have to choose between nearly 10 people for every job.
A Waitrose spokesman said it was an ‘incredible’ response.
Opportunities at the Waterside site range from roles in the customer café and delicatessen, meat and fish counters to the checkouts and shop floor.
Applications for jobs at the store close on Sunday (April 28).
The store is due to open in mid-summer.
All new employees at Waitrose will become partners in the John Lewis Partnership, entitling them to benefits including shopping discounts, leisure and learning subsides and an annual bonus.
Each existing partnership employee recently received 17% of their annual wage in bonus, the equivalent of nearly nine weeks wages.
Nearly £1 million is expected to be generated each year in wages and bonuses for Aylesbury employees.
Waitrose said staff will be given training to help them become experts in their area, including the opportunity to become product specialists advising customers on wines, cheese, meat, fish and fresh produce and receive management training.
The store will be 21,000 sq ft, similar to the size of the Thame Waitrose.
Anyone wishing to apply should visit the Waitrose website.