layout:
<android.support.design.widget.BottomNavigationView
                android:id="@+id/navigation"
                android:layout_width="match_parent"
                android:layout_height="wrap_content"
                android:layout_gravity="bottom"
             app:onNavigationItemSelected="@{viewModel.onNavigationItemSelected}"
                android:background="?android:attr/windowBackground"
                app:menu="@menu/menu_home_tab" />
code:
@BindingAdapter("onNavigationItemSelected")
    public static void setOnNavigationItemSelected(
            BottomNavigationView view, BottomNavigationView listener) {
        view.setOnNavigationItemSelectedListener(new BottomNavigationView.OnNavigationItemSelectedListener() {
            @Override
            public boolean onNavigationItemSelected(@NonNull MenuItem item) {
                switch (item.getItemId()) {
                    case R.id.navigation_dashboard:
                        Log.d("test","test1");
                        return true;
                    case R.id.navigation_notifications:
                        Log.d("test","test2");
                        return true;
                }
                return false;
            }
        });
    }
This returns an error
Error:(183, 49) Could not find accessor viewmodel.onNavigationItemSelected 
I am trying to implement databinding on my bottomnavigationview
Maybe it will be helpful to someone, detailed addition to accepted answer with setting selected item in xml.
BindingAdapters:
public class BindingAdapters {
    @BindingAdapter("onNavigationItemSelected")
    public static void setOnNavigationItemSelected(
            BottomNavigationView view, BottomNavigationView.OnNavigationItemSelectedListener listener) {
        view.setOnNavigationItemSelectedListener(listener);
    }
    @BindingAdapter("selectedItemPosition")
    public static void setSelectedItemPosition(
            BottomNavigationView view, int position) {
        view.setSelectedItemId(position);
    }
}
ViewModel:
public class ViewModel implements BottomNavigationView.OnNavigationItemSelectedListener {
    @Override
    public boolean onNavigationItemSelected(@NonNull MenuItem item) {
        switch (item.getItemId()) {
            case R.id.navigation_favourites:
                Log.d("testTag","Selected favourites");
                return true;
            case R.id.navigation_photos:
                Log.d("testTag","Selected photos");
                return true;
            case R.id.navigation_info:
                Log.d("testTag","Selected info");
                return true;
        }
        return false;
    }
}
Layout with BottomNavigationView:
<?xml version="1.0" encoding="utf-8"?>
<layout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    tools:context=".views.MainActivity">
    <data>
        <import
            type="com.test.R"/>
        <variable
            name="viewModel"
            type="com.test.viewmodels.ViewModel"/>
    </data>
    <android.support.constraint.ConstraintLayout
        android:id="@+id/container"
        android:layout_width="match_parent"
        android:layout_height="match_parent">
        <android.support.design.widget.BottomNavigationView
            android:id="@+id/nav_view"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_marginStart="0dp"
            android:layout_marginEnd="0dp"
            android:background="?android:attr/windowBackground"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintLeft_toLeftOf="parent"
            app:layout_constraintRight_toRightOf="parent"
            app:menu="@menu/bottom_nav_menu"
            app:selectedItemPosition="@{R.id.navigation_photos}"
            app:onNavigationItemSelected="@{viewModel::onNavigationItemSelected}"/>
    </android.support.constraint.ConstraintLayout>
</layout>
                        You should have onNavigationItemSelected() declared in your viewModel class:
class ViewModel {
    @Override
    public boolean onNavigationItemSelected(@NonNull MenuItem item) {
        switch (item.getItemId()) {
            case R.id.navigation_dashboard:
                Log.d("test","test1");
                return true;
            case R.id.navigation_notifications:
                Log.d("test","test2");
                return true;
        }
        return false;
    }
}
In your xml, use method reference:
app:onNavigationItemSelected="@{viewModel::onNavigationItemSelected}"
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