Mr Hague succumbed to pressure from pro-European MEPs and persuaded the Shadow Cabinet to approve a plan to maintain a loose affiliation to the European People's Party (EPP).
The decision will create a coalition that can take control of the Parliament from the Socialists group and allow Tory MEPs to take up important committee chairs in Strasbourg.
The EPP has a staunchly federalist manifesto that directly contradicts the anti-single currency stance that paid dividends for the Tories in the European elections last month.
However, Mr Hague decided that he could not allow his 36 MEPs to form their own group in Strasbourg or to form a new alliance with more anti- federalist parties.
In an attempt to reassure both wings of the party, the Shadow Cabinet approved a plan that Conservative Central Office claimed had weakend the links while retaining influence. Under the plan, the Tories will seek to change the name of the EPP to "EPP and the Conservatives Group" and MEPs will take the whip from Westminster rather than Strasbourg. The Tory group will not be committed to the EPP constitution, which explicitly supports a "United States of Europe".
Pro-Europeans pointed out that the Tories are not currently bound by the EPP manifesto and that has not changed.
The EPP has to sanction the name change at its congress in Marbella, Spain, next week.