Hills had been in caretaker charge of the England Women's team following the sacking of Hope Powell, whose permanent successor was confirmed as Mark Sampson earlier this month.
The FA also revealed that Marieanne Spacey will take up the role of assistant women's coach and coach developer.
Hills said: "My experience in long-term player development and international coaching will help me work with all those in elite player development to improve the quality and quantity of female international players over time.
"I am very much looking forward to working with the new senior head coach Mark Sampson and his international staff in order to support the senior squad."
As well as working alongside Sampson, Spacey will take charge of the U23 team, and she said: "This is a huge opportunity for me.
"I think my various roles are really important for the future of women's football in this country and I am really looking forward to the challenge.
"The prospect of working with two different England squads really excites me, as does helping any female player that wants to become a better coach, because we need more female role models across the game."
FA director of football development Sir Trevor Brooking added: "Mark, Brent and Marieanne have already spoken and they are all extremely excited by the prospect of working together.
"We believe they will complement each other and mix really well to take the game forward at every level and build on the good work that has gone before."