Hi,
I have to control a 24V, 350W DC Motor.

link: https://robokits.co.in/e-bike/e-bik...-300rpm-350w?zenid=thhuodifpf22tvvag1tbkopm97

I have selected the below driver:

https://www.pololu.com/product/2995


Before buying this driver I just want to make sure that I can program it with arduino and it can control the motor.
I need to control Motor directions and speed. Please make me sure that it will be suitable for my application .

 

It does look OK. But I'd set the hardware current limit lower that the 50Amps default. Try a 47K resistor between Vef and GND to set about 20Amps max.
These boards look OK on paper but the proof is in the testing. Try to see if you can blow one up by stalling the motor and reversing it at speed.... These things can happen in real life.
What is the motor load going to be?

 

The motor is going to rotate a gear box of gear ratio 20:1.