Customers will receive the gift card if they trade in their working iPhone 5, iPhone 4s or iPhone 4 and purchase the iPhone 5s or iPhone 5c with a two-year contract.
The iPad offer is less restrictive: Customers will receive a minimum $100 Best Buy gift card when they trade in any working iPad.
Customers can trade in their devices at Best Buy and Best Buy Mobile specialty stores. Devices must power on to be considered working, and those with cracked screens or water damage are not eligible.
Best Buy's deal comes on the heels of similar moves by competitors.
In late September, Microsoft announced that it would give a minimum $200 gift card to consumers who traded in their gently used iPhone 4s or iPhone 5 devices. The catch, of course, is that the gift card is for Microsoft retail stores.
Target, meanwhile, is running its own Apple sales promotions during Black Friday weekend. The deals, which begin Nov. 28 and run through Nov. 30, include a $75 Target gift card with the purchase of a $299 iPad Mini Wi-Fi 16GB and a $100 gift card with the purchase of an iPad Air Wi-Fi 16GB.