Emily Price, from Huntingdon, Cambridgeshire, had recently handed in her Aberystwyth University dissertation where she studied maths and physics.
She was also due to study for a Master's degree in the town next year.
The council held a minute's silence at its meeting on Monday, where Ms Price was due to make her declaration to become a councillor.
She was taken ill after being elected to the town's central ward, representing the Liberal Democrats.
Ceredigion MP Mark Williams posted a photograph of Ms Price on Twitter and wrote: "Terribly sad news today. We have lost a truly wonderful member of our Liberal family here in Ceredigion. RIP Emily."
Ms Price was also the incoming vice chair of the Welsh Young Liberals, IR Cymru.
Mark Cole, Honorary President of IR Cymru, said: "She will be greatly missed by all who knew her but she will be remembered with great fondness and love for everything that she achieved in her tragically short life and for everything that was left undone.
"Emily's time with us may have been heartbreakingly short, but what she gave to those around her will inform, inspire and motivate her friends for the rest of their lives."
He added Ms Price was a "real character" and a "beloved member" of the Aberystwyth University students' group, of which she was a former president.
"I was delighted when Emily herself was elected to Aberystwyth town council... she was going to contribute so much more to the civic life of her university town."
An Aberystwyth Students' Union spokesperson said: "Her passing will be deeply felt by many and our thoughts go out to all those who are close to Emily."
Prof Qiang Shen, director of the Institute of Mathematics, Physics and Computer Sciences, said: "Emily had a particular interest and talent in communicating science to young people and encouraging them to study the subjects that she cared about so much.
"She was always the first to volunteer as a student ambassador and to help with outreach events within the university and at schools and festivals.
"With her quiet smile and enthusiasm, Emily will be fondly remembered and sorely missed by all her fellow students and staff at Aberystwyth."
A 22-year-old woman who had just been elected to Aberystwyth town council has died after a short illness.