This provides the high-level steps for the solution. You'll need Active Directory in order to leverage Kerberos with Windows. Then what you will do is use Java Spring Security for Kerberos in order to access the REST service from Java. The below are the more concrete steps.
The Java Spring Security for Kerberos library will do the heavy lifting for you, this provides a class to inject a Kerberos configuration into the HTTP client: org.springframework.security.kerberos.client.KerberosRestTemplate
You define some Kerberos properties within a client configuration .properties file. Here's the most important snippet from the file with respect to Kerberos:
KERBEROS.FLAG=Y
KERBEROS.DEBUG=true
SERVICE_ACCOUNT_PRINCIPAL = HTTP/some.hostname@YOUR.REALM
KEYTAB_LOCATION = file:///C:/path/to/filename.keytab
KDC = server.fqdn.name
KDC_DOMAIN = YOUR.REALM
KRB5 = file:///C:/path/to/krb5.conf
EDIT:
Kerberos keytabs are not required with a Java client on a Windows AD domain-joined machine. Since you want to use the credentials of the person who is running the Java program, you wouldn't use a keytab (since the keytab itself contains only one credential).
Refer to the official Spring Security Website