Patrick Chinskie, 47, raped five different women over a 23-year period. Some of the offences took place in Govanhill and other parts of the city.
At the High Court in Edinburgh, judge Kenneth Maciver, QC, told him: "These crimes form a virtual unbroken chain of offending from 1990 to 2013."
Under a Lifelong Restriction Order the court sets a minimum period the offender must serve in jail but any future release, if at all, is left to the parole authorities.
The judge continued the case until October.