There are a couple of ways to do this.
One is to create a data flow with a Derived Column Task. Then you can pull in both variables and send it to a OLE DB or SQL Server Destination.
Another is to use a Execute SQL Task. The trick part of this is using the parameters correctly. The query would look like:
IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'dbo.[VarLog]') AND type in (N'U'))
DROP TABLE dbo.[VarLog]
Create table dbo.varlog (
[var1] [varchar](50) NULL,
[var2] [varchar](50) NULL
)
Insert into varlog (var1,var2) values(?, ?)
On the Parameter Mapping Screen add your two variables. Note that the Parameter Name is a 0 based counter that corresponds to the ?. See screen show for example. In my test I used the system variables for PackageName and StartTime.
Note: I opted to drop and replace the table for the example. Most likely you will want to have this static and maybe add a datetime to the table to track the vars over time.
Note2: I know start time isn't a varchar but it serves the purpose of the example.