If you still have access to your exchange account, just export the contacts as a vCard, then proceed to go to https://www.icloud.com then log in with your apple id and password. Proceed to contacts, then on the bottom left corner of the browser you should see a cog wheel, select the cogwheel, and then import said vCard. Now you should have all those contacts in icloud and therefore in your contacts.
Question: I have contacts stored in my phone that are associated with a Microsoft exchange email account. How do I get those onto my iCloud so i can delete those email accounts?