In a Galvanic cell, the electrons flow from 

In galvanic cell, the Zn(s) looses  its electrons to form Zn²⁺ ions. 
The electrons remain behind on the Zn electrode. As the Zn is oxidized, the Zn electrode is the anode.  
The electrons flow through an external circuit to the copper electrode. 
As Cu²⁺ is reduced the Cu electrode is the cathode. 
Hence galvanic cell, electrons flow from anode to cathode through an external circuit.