He hopes to have done so in a way that will circumvent the traditional Labour charge of 'betrayal'. His key philosophical statement came early in the campaign when he defined left thinking as having been dominated by two strands - the 'ethical socialism' of European social democracy and the class-based economic determinism of Marxist thought. He came, he made clear, from the former - 'the only serious view of the left's future that can remain'.
He argued that once socialism is defined that way - as a set of principles and beliefs - 'then it can liberate itself, learning from its history rather than being chained to it. It then no longer confuses means, for example wholesale nationalisation, with ends - for example a fairer society and more productive economy. It can move beyond the battle between public and private sector and see the two as working in partnership. It can open itself up to a greater pluralism of ideas and thought'.
In terms of policy, what that has translated into during the campaign is chiefly positioning rather than much in the way of hard and fast commitments beyond those already in Labour's programme.
Mr Blair has acknowledged firm limits on the ability of national macro-economic policy to alter the economy's potential for long-term growth. However, supply side measures such as education and training, tax changes to support research and development, and a tax regime on share ownership aimed at encouraging long-term investment rather than short-termism, can all strengthen its underlying performance, he argued.
A more radical change than the Government has so far agreed on the rules allowing private finance into public sector projects should also be examined, he has said.
On jobs, Mr Blair has backed the 1944 White Paper definition of 'high and stable' employment, stating that 'the goal of full employment' is 'the objective of any decent society'. He has rejected targets or timetables, the approach John Prescott initially advocated, declaring: 'I am not going to make promises I can't keep.'
Like Mr Prescott, however, he has focused both on youth unemployment and on the long-term unemployed, saying the eradication of that should be 'a central goal'. He wants to 'build on' Labour's plans for a year's National Insurance rebate for employers who recruit the long-term unemployed, for the phased release of councils' capital receipts, and for a new environmental task force combining work experience and training for the young.
He has backed a minimum wage - but again as a principle. And he has promised to change a tax system which is 'a haven of scams', allowing those with accountants to pay little or no tax while others pay more than their fair share.
Education and training 'hold the key, not just to personal fulfillment and advancement, but also to economic prosperity and a good society'. He has argued 'the more we put into education, the more we shall get back'. That meant universal pre-school education with a continued national curriculum, better forms of testing and assessment, and comprehensive schools that offer education for all the talents. He also supports teacher associates - people from business, industry and the professions bringing outside expertise into schools to help teachers - while promoting 'personalised skills accounts' for adults.
On welfare, Mr Blair has attempted to redefine for Labour, ahead of the report of its Social Justice Commission, what social security should be about, seeking a system that 'provides a springboard to success and not a road to dependency'. That meant moves to remove disincentives to paid work, easing the transition between in work and out of work benefits, and attempting to end a situation where when a man loses his job there is no point in the woman continuing to work.
On Europe, he has said it is 'both time to stand up for Europe and to re-think its progress' - indicating firm support for a single currency provided the conditions are right. The message was strong that a Blair-led Labour Party would be a pro-Europe party. That, however, was coupled with a warning that 'the next stage of European progress will come through persuasion or not at all.'
And he has made the constitution a centre-piece of his platform, arguing that constitutional reform is not 'a subject elevated from the daily experiences of British citizens' because 'it matters who's got their hands on power.'