You can migrate an RDS instance from one VPC to another VPC. Firstly, you have to switch the network type of the RDS instance to the classic network, and then switch it to the VPC.
The VPC switch will cause an ephemeral disconnection for the RDS instance. Ensure that you have set an automatic reconnection mechanism for it.
Log on to the RDS console.
Switch the network type to the classic network:
Click the ID of the target RDS instance.
On the left-side navigation pane, click Database Connection.
In the Connection information section, click Switch to Classic.
Click OK in the pop-up dialog.
Switch the network type to VPC:
Click Refresh to check the database status.
After the network type is changed to the classic network, click Switch to VPC.
In the pop-up dialog, select a new VPC and VSwitch for the RDS instance and then click OK.
Add the new private IP address to the RDS whitelist, see Set whitelist.
Restart the RDS instance.