Anderson has been rewarded for his Scottish Cup final goal against Dundee United last weekend with a new two-year deal and he will celebrate his testimonial year with the Perth club early next season.
Miller and back-up keeper Stevie Banks, meanwhile, have been handed new 12-month agreements, and Saints boss Tommy Wright is happy to keep the trio.
"Ando has agreed the new contract," said Wright in the Daily Record. "That's brilliant news and he can look forward to a great testimonial year.
"Gary moans that he doesn't get enough games but he's made 50 appearances in two seasons. I like that he isn't happy and moans."
However, Wright has decided not to renew the contracts of Nigel Hasselbaink, Paddy Cregg, Tim Clancy or Chris Iwelumo, who all now leave the club.