hibernate should make the transition seamless for you.
Make sure to choose the correct driver as some drivers might act differently.
I personally like jtds. It has vast documentation.
Look for native queries in your code because they might need some modifications.
Other than that, I don't think you should experience any problem.
I had an application that supported oracle, SQL-Server and mysql and we didn't have specific code for each one.
EDIT : as maba suggests in the comments, you will need to modify the hibernate configuration a bit (driver, dialect, url ).
For more hibernate specific configuration, I found a great stackoverflow answer