Ms Kluk's bound and gagged body was found concealed in the church after Tobin, a convicted sex offender, fled to London after attacking her last September, sparking a nationwide manhunt.
He had claimed in court that he was not responsible for her death and that she had consented to having sex with him.
As Tobin was led from court today he attacked a press photographer, before being separated from the man by police officers.
A statement from Ms Kluk's sister Aneta and father Wladyslaw said the student's family were "relieved" that Tobin was behind bars.
"We would both like to thank all of the Scottish public for their support during this horrific time and would now ask that our privacy is respected and that the media allow us to grieve in private," Aneta Kluk said.
Strathclyde police Detective Superintendent David Swindle described the case as one of the most "harrowing" he has had to deal with.
He said that he hoped Ms Kluk's family could "now start to rebuild their lives and feel that justice has been done".
"I am fully aware that members of the media have many questions regarding Peter Tobin's background. However, due to legal restraints, I am unable to discuss these matters at this time," he continued.
"This has been a traumatic ordeal for all those connected with Angelika. I have no doubts that this will live with them for the rest of their lives but hopefully this has brought some closure."
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