Changing the background color of a Tab in TabLayout (Android design support library) doesn't occupy the entire tab space

Define a selector as a drawable, and also have a drawable for the selected/unselected states.

For this solution, I started with the code from this answer, and then added the functionality that changes the background color for the current Tab.

First, the selector, tab_background.xml in the drawable folder:

<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
    <item android:drawable="@drawable/tab_background_selected" android:state_selected="true" />
    <item android:drawable="@drawable/tab_background_unselected" android:state_selected="false" android:state_focused="false" android:state_pressed="false" />
</selector>

Then, tab_background_selected.xml in the drawable folder:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android" >
    <solid android:color="#d13fdd1a" />
</shape>

Then, tab_background_unselected.xml in the drawable folder:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android" >
    <solid android:color="#3F51B5" />
</shape>

Finally, in your styles.xml, specify the selector to use, and also specify the tab indicator style, since the app:tabIndicatorColor property in the TabLayout will now be ignored:

<style name="Base.Widget.Design.TabLayout" parent="android:Widget">
    <item name="tabBackground">@drawable/tab_background</item>
    <item name="tabIndicatorColor">#ff00ff</item>
    <item name="tabIndicatorHeight">2dp</item>
</style>

Result with the example colors above:

Additional Note:

Tested with the 23.3.0 versions of the support library components:

dependencies {
    compile 'com.android.support:appcompat-v7:23.3.0'
    compile 'com.android.support:cardview-v7:23.3.0'
    compile 'com.android.support:recyclerview-v7:23.3.0'
    compile 'com.android.support:design:23.3.0'
    compile 'com.android.support:support-v4:23.3.0'
}

you should use:

app:tabBackground="@drawable/tab_selector"
android:background="@color/colorNormal"

tab_selector.xml (in Drawable Folder):

<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
    <item android:state_selected="true" android:drawable="@color/colorSelected"/>
    <item android:state_selected="false" android:drawable="@color/colorNormal"/>
</selector>

Tabs with Ripple effect: In addition to Daniel Nugent's answer It would be beautiful to add a ripple effect to tabs. In order to achieve this, you must add these two drawables to drawable-v21 folder:

tab_background_selected.xml :

<?xml version="1.0" encoding="utf-8"?>
<ripple xmlns:android="http://schemas.android.com/apk/res/android"
    android:color="#63D25B"> <!-- ripple color -->
    <item android:drawable="#d13fdd1a" /> <!-- normal color -->
</ripple>

tab_background_unselected.xml :

<?xml version="1.0" encoding="utf-8"?>
<ripple xmlns:android="http://schemas.android.com/apk/res/android"
    android:color="#606FC7"> <!-- ripple color -->
    <item android:drawable="#3F51B5" /> <!-- normal color -->
</ripple>