Williams won her seventh Wimbledon title with a 7-5, 6-3 win over Graf’s German compatriot Angelique Kerber at the All England Club on Saturday.
“What an incredible performance by Serena at Wimbledon,” Graf wrote on her Facebook page.
“Such a gift to all sport fans who get to continue to watch her add to an already amazing career #22!!!
“Also, well done to Angelique making Germany so proud with her talent and fighting spirit!”
Men’s world number one Novak Djokovic, who saw his title defence end in a shock third-round defeat to Sam Querrey, also tweeted his congratulations.
The Serb concentrated on the number 22 rather than the American’s age of 34.
“@serenawilliams loves being 22. So young and successful. Well done Rena!” tweeted Djokovic.