Production notes

The film marked Bergman's return to working for a Hollywood studio after several years of working in Italy with her husband, Roberto Rossellini. (Their marriage had caused a scandal, as he divorced his then current wife, Marcella DeMarchis to be with her.) The film was also a comeback for Helen Hayes. She had suspended her career for several years due to the death of her daughter Mary, and her husband's failing health.

Exterior filming for Anastasia took place primarily on-location in Paris, with a second unit capturing location footage of Copenhagen. The Alexander Nevsky Russian Orthodox Cathedral in Paris, which was a center of worship for Russian aristocrats and other émigrés from St. Petersburg in the city, is featured in one of the early scenes. The studio interiors were shot at MGM-British Studios at Borehamwood, England. Knebworth House was used to represent the Empress Marie's palace.

The film received generally positive reviews from critics. The review aggregator website Rotten Tomatoes reported that 92% of critics have given the film a positive review based on 52 reviews. On Metacritic, the film has an average score of 61 out of 100 based on 19 reviews, indicating "generally favorable" reviews. Mae Tinee of the Chicago Tribune called the film "Beautifully balanced with history and fantasy woven into a background of searing sorrow and royal pomp, this is one of the year's most enjoyable films. It is presented with wit, warmth, delicacy, and skill." Many critics emphasized the film's status as Ingrid Bergman's comeback vehicle. Jean Yothers of the Orlando Sentinel wrote "After an absence of seven years from American-made films, beauteous Ingrid Bergman returns triumphantly." Moira Walsh of America wrote "Given a chance, Miss Bergman looks as lovely as ever and gives an effective high-tension performance." Some critics believed the film was bound too much to the static settings and theatrical "scenes" of the play, but additional, essentially decorative, ball scenes were added to open up the action.