Offer congratulations to the high school graduate by using phrases like, "Congratulations on graduating, and best wishes for the next adventure." It's also suitable to express a wish to celebrate with the graduate.
In addition to showcasing support to the graduate via expressing congratulations, it's also acceptable to say other phrases that express love and happiness for the person. For instance, say "with love and pride" to demonstrate what it means that they were able to accomplish such a large goal. Mentioning excitement for their future plans can also be suitable, particularly if they are planning to attend college.