Upgrading nikon d40 to a d7000?

I have had my D40 for about 5 years now and i think i may finally upgrade this year to a D7000. I plan on just buying the d7000 body, but i just want to make sure that the lenses i currently have are compatible with the d7000. I have a AF-S Nikkor 18-55mm (kit lens - i don't tend to use this often), a AF Nikkor 50mm 1.8 (pretty much never leaves my D40) and a Tamron AF 70-300mm - will these lenses also work on the D7000?
i mainly want to upgrade to the D7000 for the low light performance and also for the HD video, and i want to make sure i won't regret buying the D7000!

Added (1). Thank you very much! I've had a very quick look at the D5100 and it looks pretty good too, has everything i'm looking for in this upgrade and the price difference from the D7000 is huge so i will definitely have a better look at the D5100!

Yep, all of those lenses will work w/ the D7000, but the 18-55 and 70-300 you have aren't all that great. You should consider the D5100 1) so you have more money to put towards lenses and 2) the articulating screen will help w/ videos. But if you're really dying for auto focus w/ your 50, the D7000 will auto focus with the 50 and the 5100 won't.

You just need the body, all the lenses you have will work perfectly.

Not only will all your lenses work, you can now buy inexpensive, legacy Nikkor AF lenses

Moving up from an entry level D40 to entry level D5100 is not really an upgrade. The D7000 has environmental seals and a magnesium core that the D5100 does not have