Burrows, 20, has put pen to paper a one-year deal with an option to extend depending on appearances.
Yeovil boss Paul Sturrock told the club’s official website: “Jamie had a two-year youth contract at Rangers and progressed to receive a one-year professional deal.
“Unfortunately he broke his ankle early in the season and played very little last season.
“A friend of mine gave me the quote ‘he is either smelly or Pele’ and it will be my job to make sure he is more Pele than smelly.
“I have seen enough of Jamie’s highlights and had my cards marked by several other people about what this boy can potentially achieve.”