Disney's (DIS) - Get Report highly-anticipated new streaming service, Disney+, has already snagged more than 10 million subscribers since its launch on Tuesday, according to a report from CNBC. 

Disney' shares were up 5.5% to $146.17 on Wednesday after the report came out, while Netflix (NFLX) - Get Report shares fell 2.8% to $283.87.

Wedbush Securities analyst Dan Ives said in a note that the number of sign-ups is "considerably higher than we and many on the Street were anticipating." He added that "this speaks to the 1-2 punch of success that [Disney CEO Bob] Iger and Disney have coming out of the gate with unmatched content and a massive brand/distribution that makes the House of Mouse a legitimate streaming competitor on Day One to Netflix and could hit its long term sub targets by 2024 (60 to 90 million subs) potentially two years earlier at this pace in our opinion."

Analysts for Jim Cramer's Action Alerts Plus Portfolio, which owns Disney, wrote that "we pulled some old sell-side notes to get a feel for where Street expectations were, and we found that some called for 5 to 7 million total subs in its first quarter with around 15 million by the end of its first year." The stronger-than-expected launch led the analysts to note, "don't be surprised to see DIS analysts raise estimates and price targets with this information in hand."

Users had difficulties signing up for the service and accessing content, but that apparently didn't stop users from signing up in droves. Disney is offering a free seven-day trial for the $6.99-a-month service, and Verizon (VZ) - Get Report wireless unlimited customers also were receiving a free year of access, so it's unclear how many of those 10 million plus customers will actually become paying customers. 

By comparison, at the end of the third quarter, Netflix had 158 million worldwide subscribers, about 60 million of which were in the U.S.

Ives wrote in his note that Disney+'s early success and the recent entry of Apple (AAPL) - Get Report TV+ meant that he believes "that 10%+ of Netflix's installed base could be disrupted/[subject to] higher churn by these two stalwarts entering the streaming landscape."

Disney and Apple are holdings in Jim Cramer'sAction Alerts PLUS Charitable Trust Portfolio. Want to be alerted before Cramer buys or sells these stocks? Learn more now.