For Twitter, it appears that the microblogging service's new relationship with Apple is paying off.

The company saw a huge boost in user sign-ups on the first day of iOS 5 being live, thanks to an especially tight integration between the service and Apple's ever-popular mobile operating system. Last Wednesday, when iOS 5 was officially released, Twitter had three times the new user sign-ups it normally sees in a typical day, CEO Dick Costolo told the crowd at the Web 2.0 Summit yesterday.

As owners of iPads, iPhones and iPods rushed to download the new operating system last week, many of them who hadn't yet signed up for Twitter were faced with a new incentive to do so: The service is now tied directly into the OS of the devices they use everyday. Why not check it out?

The company's partnership with Apple has paid off even more than expected, Costolo said. He touted the significance of their relationship, calling Apple a "corporate mentor." In signing on with Twitter for this integration, Apple bypassed Facebook, whose user base is many times larger than Twitter's, presumably due to recent tensions between the two tech giants. A Facebook-Apple integration likely would have seen far more immediate adoption, thanks to Facebook's 800 million users. By comparison, Twitter has about 200 million users, only half of which are active.

Early Success For iOS 5 and iPhone 4S Has Helped

iOS 5 itself has done quite well, if early numbers are any indication. Not even a week after its release, Apple announced that more than 25 million people were using iOS 5.

The Twitter sign-up numbers cited by Costolo only included the first day of iOS 5's release, so it remains to be seen how things looked for Twitter two days later when everybody got their hands on the new iPhone 4S. The device sold 4 million units in its first weekend, which blew away records set by the iPhone 4 last year.

On top of that, at least 20 million people downloaded iOS 5 and installed it on other, older devices. While there were certainly quite a few Twitter users among them, we have to imagine that a large number of non-users have encountered the Twitter sign-up screen for the first time via iOS 5 as well.

ReadWriteWeb's Jon Mitchell is on the ground at the Web 2.0 Summit. You can follow his continuing coverage here.