The Russian tennis player personally delivered a package containing a pair of Adidas shoes and a gym bag to US customer Dr Andrea Fineberg. Other stars including Harrison Ford and Moby will also be delivering orders.
Webcasts of the deliveries are available on the Amazon website here.
"We are excited to celebrate our 10th anniversary with these special thank you surprises for our customers," said Amazon.com vice president Kathy Savitt.
"Amazon.com and UPS will continue to surprise customers with these special deliveries until 16 July, so you might see us on your doorstep."
Michael J Fox has delivered a copy of his autobiography, Chris Noth has reprised his role as Mr Big by delivering a Sex and the City box set, and Jeff Bridges has handed over a copy of The Big Lebowski.
Latest Tesla news: Tesla stock price tanks amid reports of 'widening probe' by SEC and claims the base Model 3 loses money
SEC 'probe' takes its toll on Tesla as new research suggests that Tesla loses $6,000 on every $35,000 Model 3
10nm Cannon Lake Core i3-8121U CPUs make a rare outing with Intel's NUC mini PC
'Notorious' Australian child hacker thought he had executed 'flawless' hack
The former employee says that Tesla fired him for bringing the accusations to management internally