Amazon is exiting the 2013 holiday season with “tens of millions” of Amazon Prime members, according to a statement this morning from CEO Jeff Bezos — signaling that the company has reached at least 20 million members for its $79/year subscription program.

Overall, Amazon says the 2013 holiday season was its “best ever,” with more than 36.8 million items ordered on Cyber Monday alone. It isn’t a surprise that the holiday season set a new record, given the steady growth in e-commerce sales worldwide. The company didn’t disclose sales figures, so the full impact won’t be apparent until Amazon reports fourth-quarter earnings.

Bezos’ Amazon Prime statement, however, is significant because it’s the closest the company has come to giving an official count for its annual membership program. An an estimate by Consumer Intelligence Research Partners put the total at more than 16 million as of Sept. 30, but Amazon usually keeps the official number under wraps.

Amazon said in a news release, “Prime was so popular this holiday, that Amazon limited new Prime membership signups during peak periods to ensure service to current members was not impacted by the surge in new membership.”

One potential factor in that surge: Amazon’s decision this fall to raise the limit for free Super Saver Shipping (for non-Prime members) from $25 to $35, which may have caused more customers to consider Prime membership, for its core benefit of free shipping.

The growth in Prime membership has meaningful implications for the company, given the key role that Amazon Prime plays in generating repeat business and customer loyalty for Amazon. Prime members receive free two-day shipping on eligible items, in addition to Prime Instant Video streaming and Kindle book borrowing.

Amazon said this morning that it added 1 million Amazon Prime members during the third week of December alone, in the build-up to Christmas.

“Amazon Prime membership continues to grow, and we now have tens of millions of members worldwide. They benefit from all-you-can-eat free two-day shipping on millions of eligible items and our members have a voracious appetite,” said Bezo in Amazon’s post-Christmas news release this morning. “We are extremely grateful to our customers around the world and wish everyone the very best for the coming year.”

The company noted that a record number of Prime items were shipped on Amazon’s peak shopping day. That was part of an overall spike in shipments that overwhelmed UPS and FedEx, causing delays in some Christmas packages.

A company spokeswoman said via email this morning, “Amazon fulfillment centers processed and tendered customer orders to delivery carriers on time for holiday delivery. We are reviewing the performance of the delivery carriers.”