The 18-year-old defender, who came through the youth system at the Walkers Stadium, trained with the League One club on Monday and will go straight into the squad to face Hartlepool on Tuesday night.
"I have been at Leicester for three years and this is the start of senior football for me now," Bolger told Rovers` official website.
"I am a big, tough, old-school defender but I am good at passing the ball and I have scored a few goals for the youth team at Leicester.
"The lads have been very welcoming and I can`t wait to be involved. I am looking forward to making my League debut and getting as many senior games under my belt as possible."