Rayner is the third person to hold the shadow education secretary post in the past week, following resignations from a string of shadow cabinet members opposed to the party's leader Jeremy Corbyn.
Glass replaced Lucy Powell as shadow education secretary after she resigned last weekend. However, Glass resigned from what she described as her "dream job" just two days later saying the "situation is untenable".
Corbyn has said he intends to stay on as Labour leader despite a vote of no confidence from Labour MPs going against him by 172 votes to 40.
Rayner became the the first woman to represent the North West constituency in Parliament when she won a 10,756 majority at the 2015 general election.
She has been an opposition whip and shadow pensions minister on Labour's frontbench team, and served on the communities and local government committee from July to October last year.
Before becoming an MP she worked as a trade union official, and had previously been a domiciliary carer. She is married and has three children.
In her maiden speech to Parliament, Rayner said: "A care worker becoming an MP; that's real aspiration for you. Perhaps too, I'm the only member of the house, who at age 16, and pregnant, was told in no uncertain terms, I'd never amount to anything. If only they could see me now."
In November last year, Rayner made headlines for writing a letter of complaint to a shoe shop using House of Commons-headed paper.