The process for share transfer remains the same - fill ICICI Direct’s DIS Slip(Delivery Instruction Slip) with an instruction to transfer shares to Zerodha. Mention your Zerodha Demat DP ID and Client ID in the slip. The slip has to be signed by the first holder and the second holder in this case.
This is Zerodha’s DIS slip along with instructions on how to fill it. If you have a CDSL account with ICICI Direct then the DIS slip will be similar. You can follow the same instructions to fill their slip.