The transaction fee is received by the bitcoin miner. When a new bitcoin block is generated with a successful hash, the information for all of the transactions is included with the block and all transaction fees are collected by that miner creating the block, who is free to assign those fees to himself. Traditionally, the sender pays the full Bitcoin network fee; deducting the fee from the amount received by the recipient will often be considered an incomplete payment, although some wallets have a "sender-pays-fee" feature where the miner fee is deduced from send amount.