How to call .dtsx package file which has input parameters from a stored procedure?

Stored Procedure # 1 -> Will pass the list of files to be exported to excel as a Comma Separated value in a variable.

Input variable will be passed to the SSIS Package to export the data to excel.

How to handle the SSIS Package which has Input parameters from a Stored Procedure call?

Using DtExec and xp_cmdshell

One way to do that is to run DtExec utility from file system using xp_cmdshell utility inside sql server.

First you have to enable the xp_cmdshell utility:

-- To allow advanced options to be changed.
EXEC sp_configure 'show advanced options', 1
GO
-- To update the currently configured value for advanced options.
-- WITH OVERRIDE disables the configuration value checking if the value is valid
RECONFIGURE WITH OVERRIDE
GO
-- To enable the xp_cmdshell component.
EXEC sp_configure 'xp_cmdshell', 1
GO
RECONFIGURE WITH OVERRIDE 
GO
-- Revert back the advance option
EXEC sp_configure 'show advanced options', 0
GO 
RECONFIGURE WITH OVERRIDE 
GO

Then you can use the following command to execute the package and pass avariable value as parameter:

DECLARE @SQLQuery AS VARCHAR(2000)

DECLARE @ServerName VARCHAR(200) = 'ARSHAD-LAPPY' 

SET @SQLQuery = 'DTExec /FILE ^"E:\DataTransfer.dtsx^" '
SET @SQLQuery = @SQLQuery + ' /SET \Package.Variables[ServerName].Value;^"'+ @ServerName + '^"'

EXEC master..xp_cmdshell @SQLQuery
GO