The 18-year-old's new tune was written following her time in rehab last year, and marks a new beginning for Lovato.
Skyscraper was first played yesterday - and Demi's fans - including several celebrities - took to their Twitter pages to congratulate her on the song.
Reality star Kim Kardashian wrote: 'So excited 2 download [Demi's] new song Skyscraper! It's out tonight! Everyone Must Download It! So proud of u Dem!', while Desperate Housewives actress Eva Longoria added: 'Me Too!'
And the former Sonny with a Chance star was overwhelmed by all the support she received.
She wrote: 'Okay I'm literally balling my eyes out right now... So grateful for my friends and fan's support.. Wow... So happy, so blessed...'
Demi later added: 'Wow.. Top 10 on iTunes within a matter of hours?!? Definitely can't sleep now. Unbelievable.. Never underestimate my #LOVATICS! #SKYSCAPER.'