In December 2009 a handful of music bloggers received an email from an anonymous account. The email had a link to a YouTube video called – rather snappily – Prelude 699130082.451322-5.4.21.3.1.20.9.15.14.1.12. In it, a naked woman was glimpsed curled up in a swirl of jet-black liquid, intercut with shots of blackened limbs emanating from giant oak trees while a soundtrack of ambient electronica burbled in the background. It turned out to be the first of six Prelude videos, generating a level of online intrigue that big-name pop stars can only dream of.

With each new wonderfully creepy clip came more questions: What did the numerical titles mean? What was the significance of all the animal imagery? Why did the woman seem to be licking semen off a tree? And, most importantly, who on earth was this enigmatic siren? Names bandied about on music forums included high-concept pop stars such as Lady Gaga, Björk and, er, Christina Aguilera.

As it turned out, our mysterious semen-licker was a Swedish singer-songwriter called Jonna Lee, in the process of reinventing herself as iamamiwhoami. Her transformation has been so convincing that, when I arrive to meet her in an ultra-modern west London hotel, it feels most incongruous. We should be in a forest, making pagan symbols out of twigs, surrounded by familiars. But with the lights off and the curtains drawn I find Lee, dressed head-to-toe in black with a shock of white hair, stood peering out of the first floor window at a fox that's curled up outside in the mid-afternoon sun. It stays there for the duration of the interview.

Kin video still. Photograph: John Strandh

I accuse Lee of summoning it here to keep an eye on us. "Hmm, yes," she says slowly, her blue eyes framed by massive fake blonde eyelashes.

In fact, "Hmm, yes," is Lee's default setting when it comes to ending sentences. This is the first proper interview she's done under the guise of iamamiwhoami, and there's a sense that she'd still rather not give too much away. Questions about various recurring motifs that run throughout Prelude, as well as the Bounty series that followed, and the most recent videos for songs from her forthcoming Kin album, are all politely rebuffed.

I ask her if she sees herself as the same person as the one who released two KT Tunstall-lite solo albums in her native Sweden under her birth name. "I would say I'm the same person, but I guess I've found other sides of myself," she replies. "I'm a happier person. I mean, I don't separate myself from what I do because I'm living it. Hmm, yes."

Lee defines iamamiwhoami as a multimedia "entity" – one which, alongside her and music producer Claes Björklund, includes directors, designers and close friends. Its creation was a way for Lee to submerge herself in her own world, simultaneously inviting her audience to join her while also teasing them with only snippets of information. Her identity wasn't fully revealed until the 12th video, her face initially obscured by make-up and what looked suspiciously like cellophane.

"Leaving space for everyone's imagination to run free is a big part of it," she says, "both in terms of how we communicate and also in not being overly clear what the message is. It's kind of like receiving a script for a movie and reading it while you're watching it." One of the main reasons for this lack of a defining message was the fact that Lee herself didn't really know what she wanted iamamiwhoami to be, hence the moniker. Was she aware of the fuss the early videos caused?

"Yes. It was unavoidable but I just needed to close the door around me and think, 'OK, let's focus on this,' because I needed to develop it as some sort of form. I had to work out if it was reality or a brief moment. I knew that once all the talk had settled, the work would still be there, and I wanted to create a world where I could stay."

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While her videos are typically uploaded within weeks of completion, opening up a direct line of communication between artist and audience, there's still a sense of barriers being raised. In November 2010 she let one "lucky" person into her world after appealing to her fans to find a representative to appear in To Whom It May Concern, an hour-long webcast that opened with Lee driving off with the sole audience member in a battered Volvo and performing for him from the top of a man-made pyramid of cardboard boxes before luring him into a coffin and seemingly burning him alive. "It was just the way it had to be, I'm sorry to say," Lee explains. "Now may he rest in peace."

There's a glint in her eye that returns when I tell her I'm concerned about the fact that a black cat that starred in a number of early videos seems to have disappeared. "Everything has its purpose and sometimes things fade away slowly and sometimes they reappear," she purrs.

For all their intellectual posturing – the Prelude videos deal extensively with the myth of the mandragora officinarum, which claims that the semen of a hanged man produces the hallucinatory root – there's humour buried within. In the video for Play, for example, ridiculous-looking yetis dance around with a semi-nude Lee to the song's drip-feed R&B, looking like Hype Williams directing a racy episode of Harry And The Hendersons. Then there's the merchandise. Released to coincide with her debut album Kin, you can now buy iamamiwhoami pants. Apparently this is "a comment regarding the way we consume things" and fits "into what it needs to be for people to grasp it". Is she saying we'll understand where she's coming from once we pull on a pair of her kecks? "I think, definitely," she says. "I can't imagine anything more sexy than that."

Kin video still. Photograph: John Strandh

Sex seems to be on Lee's mind today, albeit in a typically abstract way. I ask her why she's decided to physically release Kin, given that the songs are already available to buy digitally and the videos have been online since the start of the year. From what I can gather, it's because when she played her first live show in front of an audience at last summer's Way Out West festival, something "happened".

"There was a close encounter with the audience that started the process of making Kin, so I felt that it needed to be touched and held in people's hands," she explains. During the show, Lee writhed around on a giant pile of loo rolls – "It was a bed," she corrects, "assigned for action" – with her back to the audience but looking at a giant screen showing their faces. Lee talks about the album's "physical birth" and the "nine months of hard labour" that it took to create it. Noticing an extended metaphor looming, I suggest that maybe now she should be looking after the baby/album. "The audience needs to care for it." Is she giving it up for adoption? "It's always going to be my baby. I'm a very proud mother. I'm just sharing it."

Given the mythmaking that's surrounded the project, it's testament to how great the songs are that Kin works equally well once stripped of its visuals. Lee's voice is delicate and otherworldly, weaving its way through warm synth blasts and creeping percussion. It's also impressive that she's managed to keep people's attention after that initial thrill of the unknown subsided.

"I wouldn't have done interviews earlier," she says, as we get up to check on the fox. "It would have all looked like a big promotional campaign. I would have been a sad person for a long time. I can't say that I would have been here now. But it's evolved in a way that we can still do it." She pauses. "Hmm, yes."

Kin is out on 10 September