Downgrade SQL Server Enterprise Edition to SQL Server Standard Edition
Kendra Little did a great article on this: http://www.brentozar.com/archive/2014/08/sql-server-edition-change-standard-edition-enterprise-evaluation/

Microsoft article on supported upgrade paths:
http://msdn.microsoft.com/en-us/library/ms143393.aspx

First, note that not all downgrade scenarios are supported (You didn't provide the exact version you are running).

Second, run this query to check if there are any Enterprise features in use (those features will not work when you downgrade).

SELECT * FROM sys.dm_db_persisted_sku_features

Third, if your downgrade isn't supported (it doesn't seem like many are), then you are essentially going to have to do a fresh install with standard edition, then migrate to the new server.