All banks in the Kingdom offer currency exchange services. Please refer to "Currencies and payments" section of the Understand page
Also, you can find the list of the of money exchangers on the following links:
Arabic: http://www.sama.gov.sa/ar-sa/BankingControl/LicensedEntities/MONEY%20EXCHANGERS.pdf
English: http://www.sama.gov.sa/en-US/BankingControl/Licensed%20Entities/MONEY%20EXCHANGERS_EN.pdf