I have an iPad and an iPhone using my Apple ID. However, since the iPhone is used almost always by my spouse, I would like her to set up her own Apple ID. Is this possible, as both devices were purchased in my name.

...the iPhone is used almost always by my spouse, I would like her to set up her own Apple ID. Is this possible...

Yes, and it's fairly easy to set up.

The summary version is for you to sign out of your account on the iPhone but also to *retain* the data on it, such as Calendars, contacts and photos. If these are retained it's not too difficult to edit them to your wife's requirements when she has completed the steps below.

Follow the instructions for signing out of your account in Apple's support document Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac. Note step 5 in the iPhone example on that page: Turn on the data that you want to keep a copy of on your device.

Then you will need to set up a new Apple ID on the phone before your wife can start to use it. See How to create a new Apple ID. The instructions advise to set this up in the App store, so scroll down to that paragraph.

Then set up family sharing to access the already purchased content.

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. If possible, also set up Family Sharing  between the IDs to keep access to your apps/purchases. 

 How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.       

What to do after you change your Apple ID or password - Apple Support.      

Family Sharing.         

Family Sharing - Set up.