Who issues the transaction of reward when a miner solves the block? I know that when I send money I create a transaction.  The transaction is unconfirmed, and then gets confirmed and the address owner gets the money in his wallet by summing up all the transaction of his public key address.

But what about the miner?

Suppose I am a miner with address x213123abcah23 and I solve a block and propagate it.  Who issues the mining reward to me?
Does Mr. Satoshi with his address send money to me or what?
The miner itself includes a special transaction in the block called generation transaction. Every block only has a single generation transaction. 

This generation transaction transfers the block subsidy plus the fees of the block to an address controlled by the miner.

For intance, if you look at block 434868, there is a single generation transaction that transfers 12.96 to address 17ggdTQzKFwrKP1zgqb5Kjuw6CpGKaE6Jrw.