Use Backup/Restore features. They are available under top 'Accounts' menu.
1) On old computer, click 'Back Up data...', and follow the instructions there.
2) Copy the backed up data folder to new computer.
3) Then on new computer, click 'Restore data' and follow the instructions.
Note: On restore, it will delete all previously entered 'ExpressAccounts' related data on the new computer.