Yes, it is possible.
Here is the link for it https://developer.android.com/guide/webapps/webview.html

First create html page and put below code in a button

<input type=button value=Say hello onClick=showAndroidToast('Hello Android!') />



<script type=text/javascript>

    function showAndroidToast(toast) {

        Android.showToast(toast);

    }

</script>

Now, create a webpage in android.

WebView myWebView;

    WebSettings webSettings;

    WebAppInterface webInterface;

        myWebView = (WebView) findViewById(R.id.webview);



        webInterface=new WebAppInterface(MainActivity.this);



        webSettings = myWebView.getSettings();

        webSettings.setJavaScriptEnabled(true);

        myWebView.addJavascriptInterface(webInterface, Android);

        myWebView.getSettings().setDomStorageEnabled(true);

        myWebView.loadUrl(Your url for that html file you created);

Now create a class which will listen to your callback
above line addJavascriptInterface() is responsible for callback

public class WebAppInterface {

    Context mContext;



    /** Instantiate the interface and set the context */

    WebAppInterface(Context c) {

        mContext = c;

    }



    /** Show a toast from the web page */

    @JavascriptInterface

    public void showToast(String toast) {

        Toast.makeText(mContext, toast, Toast.LENGTH_SHORT).show();

    }

}

Remember String is case sensitive,and android require @JavascriptInterface interface for calling android functionality