The specific words you are looking for may be "handed over". In usage, I envision something like
Dear ____,
I hope this mail finds you well. I am grateful for your time and patience in bidding for the project. However, you have been outbid by another developer for the same work, and therefore, the project has been handed to them. I once again take this opportunity to thank you for your time and effort.
Sincerely,
Signature