Vicky Phelan, who was diagnosed with terminal cancer after a false negative cervical smear test carried out as part of CervicalCheck, has herself becoming a leading campaigner following the controversy.
The HSE has said Ms Brennan's campaigning has led to a surge in the number of young women getting the HPV vaccine.
"Laura was an incredible young woman and a powerful campaigner", Minister Harris said.
Late Late Show host Ryan Tubridy said: "Laura Brennan was one of those extraordinary people who shine brightly and make friends easily with whoever they meet by sheer force of personality and natural kindness".
Uptake of the vaccine increased from 51% in 2017 - when Ms Brennan first contacted the organisation - to 70% in 2019. She did not dictate to any person nor did she speak to garner pity. "Her enthusiasm was infectious". Awesome doesn't do justice to her or her courage.
She is survived by her parents Bernadette and Larry, and a wider circle of family and friends.
Ms Phelan said the impact of Laura fronting the campaign for the HSE was profound as she was a attractive and glamorous young woman, which showed other young women "that this disease can hit younger people". "Thank you Laura for all you have done".
The legacy of HPV vaccine campaigner Laura Brennan, who died yesterday from cervical cancer, will be that she will save thousands of lives, Vicky Phelan has said.
She was awarded an honorary doctorate by UCD in recognition of her advocacy, and was named as the Clare Person of the Year by the Clare Association in Dublin.
Human papillomavirus (HPV) is a sexually transmitted disease that can cause cervical cancer and genital warts. Laura impressed so very many with her campaigning and her work as a patient advocate has had a real and positive effect on countless young women across the country. "Don't get swayed by rumours about the vaccine's safety-get the vaccine", she added.