how does anode become negatively charged in a galvanic cell as there is no positive charge on it to attract electrons from solution

The anode is the electrode at which the oxidation half-reaction takes place.

In a galvanic cell, the reaction is spontaneous, there is no external potential applied, and when the anode material is oxidized that makes the anode the negative electrode. In an electrolytic cell, it is the external potential that drives the reaction, the anode is the electrode where the oxidation reaction happens, consequently this time it is the electrode with the positive potential.