The Monklands East MP suffered a heart attack and died in the accident and emergency department of a London hospital he had visited two weeks earlier to campaign against its proposed closure.
Details of the new John Smith Centre for Public Service were released today to coincide with the 20th anniversary of his death, at the age of 55, at St Bartholomew's Hospital.
His widow Baroness Elizabeth Smith said: "The night before he died, John gave a speech at a Labour Party gala dinner in London concluding with the words: 'The opportunity to serve our country - that is all we ask.'
"It is that single phrase that encapsulates a lifetime of seeking to help others through efforts in public service.
"I am sure if he was still with us today it would trouble John greatly to find public life held in so low esteem.
"Given all he stood for, I believe John's life can still serve as an inspiration to a future generation who at present may not see the value of such work.
"I am hugely excited by this new initiative.
"The work of the centre will seek to define what public service is in the modern age, how it should be conducted and how everyone can consider contributing to it, whether in local communities or on the world stage."
The centre will open this year with the aim of encouraging debate and providing research into the value of public service.
Its objective is to persuade young people to contribute to public life and restore the reputation of public servants.
It has the backing of Professor Anton Muscatelli, Principal and Vice Chancellor of Glasgow University.
He said: "We are delighted to be part of an initiative for which we think we are the perfect home.
"John Smith was one of our most distinguished alumni. A bust of his image has pride of place in the Glasgow University Union where he debated and discussed some of the most vital issues of the day. His influence and impact were, and are, profound.
"It is clear that we now live in an age of crisis and renewal. We should focus on the opportunities for renewal and creating the institutions and ideals that can drive improvement across society.
"The John Smith Centre for Public Service will be a suitable vehicle to deliver on these aims."
The centre is being launched by the John Smith Trust which was set up by Baroness Smith to inspire leadership and promote good governance. It runs fellowship programmes for countries of the former Soviet Union as well as the Middle East and Gulf.
A director is being recruited to run operations.