Delivery Best Buy's delivery service professionals will: •Deliver, unpack and place your new appliance where requested, if accessible. •Connect basic appliances to electrical outlets or connect refrigerators to existing water lines. •Test product operation if it is at room temperature. •Level it, if required by the manufacturer. •Install any manufacturer-supplied safety hardware, such as anti-tip brackets. •Recycle your old appliance for free.
So yes, barring any extenuating circumstances, they should be able to take away your old washer and dryer.
Anything I post is my own opinion. I do not represent Best Buy in any way.