The cross-party push comes after David Cameron set out plans last week to hold an in-out referendum by 2017.
The Prime Minister said he wanted to renegotiate the UK's relationship with Europe, and then put the new package to a public vote.
The speech delighted many on the Tory right who have been demanding looser ties, but also drew warnings that Britain was "sleepwalking" towards an EU exit.
Tory strategists are planning to make the issue a key dividing line at the next general election, claiming Labour and the Lib Dems are trying to stop people having their say.
Clarke, a former chancellor and home secretary, and currently minister without portfolio - is the party's leading europhile but has kept a low profile since Cameron's speech.
He is expected to highlight the benefits of membership today, and challenge misconceptions among the general public.
MPs will discuss Britain's future in Europe this afternoon in the first Commons debate on the deeply divisive issue since Cameron's pledge to hold an in/out referendum.
Meanwhile, Germany's foreign minister Guido Westerwelle said Berlin was awaiting "concrete" proposals outlining Britain's demands but warned against giving ultimatums.
In an article for The Times, he wrote: "Yes, we need more competitiveness. Yes, we need more subsidiarity. Yes, Europe must become more democratic and transparent. And yes, Europe is not yet good enough."
Westerwelle said Germany was likely to agree with London on many issues but warned it would be "far easier to tear down the European house than to rebuild it once the damage is done".
"David Cameron is right: if Britain left the European Union, it would be a one-way ticket, not a return," he added.
"The current European settlement may not be to everybody's liking in every respect, but that is the nature of every good compromise. One thing, however, holds true for all of us: there are no rights without duties. There can be no cherry-picking. Saying 'You either do what I want or I'll leave!' is not an attitude that works, either in personal relationships or in a community of nations."