Graf replaces Sydney University Flames Head Coach Karen Dalton, who had to withdraw for personal reasons.
"I'm very happy with the appointment," Graf said.
"Any time you're selected to coach a team that will compete on an international level, it's an honour."
"Hopefully we'll do very well."
Graf led the Canberra Capitals to successive defencejobs Women's National Basketball League (WNBL) titles in 2006 and 2007, her fifth championship as a Head Coach.
Previously, Graf has been Assistant Coach of the Melbourne Tigers in the NBL (1992), Head Coach of the Sydney University Flames in the WNBL (1993-96), Assistant Coach of the Opals (1996 and 2000 Olympic Games, 1998 World Championships), Head Coach of the New Zealand Tall Ferns (2003-04) and Head Coach of the Phoenix Mercury in the WNBA (2004).
In 10 seasons as a Head Coach in the WNBL she has a record of 167 wins and 52 losses.
England hold their nerve to make it through to the World Cup Final at a sold-out Lord's on Sunday.