Hay, who joined Rangers from Glasgow City in 2017, has committed her future to the club with signing her first professional contract.
The winger returned from a long-term injury last season and attracted attention with displays which saw her voted SWPL Player of the Month for August/September.
Speaking to RangersTV, she said: “I am absolutely over the moon, it is been an ambition of mine from when I was young.
“As a player, I think it is a massive step because I have been at Rangers for a couple of seasons now and I have just tried to work so hard and to get an opportunity like this it is just something I had to grab with both hands and I am over the moon for myself.”
Women’s and Girls’ Football manager Amy McDonald said: “We’re delighted that Brogan has committed her future to the club today.
”She is a very exciting prospect and we’re happy to be able to reward her for her hard work and commitment to the club.”