Unfortunatly no it wont as they are locked to the Tesco Mobile Network. It only works the other way around....O2 into Tesco Mobile.
You would have to get the phone unlocked but bear in mind that this voids your 12 month warrenty with Tesco if you have to get it repaired at some point. You send the phone away, they realise its been unlocked, which they see as something which could damage your phone, it cant but they use that excuse, then they charge you to have it returned unfixed!
Hope this helps