If you are using Outlook 2010 on both of the systems, please follow these steps to export the contacts from the old computer first, to a CSV file:
In Outlook, click the File tab at the top.
Under Export, click Export.
In the Import and Export Wizard, click Export to a file, and then click Next.
Under Create a file of type, click Comma Separated Values (Windows) and click Next.
If you are exporting contacts for use in another copy of Outlook, choose an Outlook Data File (.pst).
Under Select folder to export from, select the contact folder that you want to export, and then click Next.
Under Save exported file as, click Browse, select a destination folder, and in the File name box, type a name for the file.
In the Export to a File dialog box, click Next.