JSON in Java has some great resources.

Maven dependency:

<dependency>
  <groupId>org.json</groupId>
  <artifactId>json</artifactId>
  <version>20180813</version>
</dependency>

XML.java is the class you're looking for:

import org.json.JSONObject;
import org.json.XML;
import org.json.JSONException;

public class Main {

    public static int PRETTY_PRINT_INDENT_FACTOR = 4;
    public static String TEST_XML_STRING =
        "<?xml version=\"1.0\" ?><test attrib=\"moretest\">Turn this to JSON</test>";

    public static void main(String[] args) {
        try {
            JSONObject xmlJSONObj = XML.toJSONObject(TEST_XML_STRING);
            String jsonPrettyPrintString = xmlJSONObj.toString(PRETTY_PRINT_INDENT_FACTOR);
            System.out.println(jsonPrettyPrintString);
        } catch (JSONException je) {
            System.out.println(je.toString());
        }
    }
}

Output is:

{"test": {
    "attrib": "moretest",
    "content": "Turn this to JSON"
}}

Use the (excellent) JSON-Java library from json.org then

JSONObject json = new JSONObject(str);
String xml = XML.toString(json);

toString can take a second argument to provide the name of the XML root node.

This library is also able to convert XML to JSON using XML.toJSONObject(java.lang.String string)

Check the Javadoc

Link to the the github repository

POM

<dependency>
    <groupId>org.json</groupId>
    <artifactId>json</artifactId>
    <version>20160212</version>
</dependency>

original post updated with new links