The carmaker said it would build two new models at its Sunderland plant following talks with the government.
Ministers have declined to confirm reports that a written promise was made to protect the company from any consequences of Brexit.
Labour said the government should set out exactly what was promised.
Speaking on BBC Question Time, Mr Clark indicated there had been no offer of financial compensation or state aid.
"There's no cheque book. I don't have a cheque book," he said.
"The important thing is that they know this is a country in which they can have confidence they can invest. That was the assurance and the understanding they had and they have invested their money."
He said the announcement was "fantastic news", particularly for the workforce as the deal secures 7,000 jobs.
The Japanese company's commitment to Britain's biggest car plant had been in doubt following the referendum on EU membership.
Mr Clark's department declined to comment on a report in the Times newspaper that he had written to Nissan's board promising to ensure that UK operations would "remain competitive" after Britain left the EU.
According to the newspaper, "Mr Clark's letter is regarded by Nissan as a promise that it will not have to bear the cost of punitive tariffs on car exports if Britain leaves the EU customs area without a free trade agreement in place".
The Nissan announcement has led to calls from other car manufacturers for similar pledges.
Toyota said it trusted the government to provide "fair treatment".
But a senior Nissan Europe executive, Colin Lawther, said the company had received "no special deal".
"It's just a commitment from the government to work with the whole of the automotive industry to make sure the whole automotive industry in the UK remains competitive," he told the BBC.
"We would expect nothing for us that the rest of the industry wouldn't be able to have access to. We see this as a whole industry thing, not a Nissan thing."
Labour leader Jeremy Corbyn said the government must disclose any deals struck with the firm, saying it could not hide it from the public.
Nissan confirmed it would build both the new Qashqai and the X-Trail SUV in Sunderland.
A company spokesman said making the X-Trail could lead to hundreds of new jobs being created in the coming years. It will be the first time the model has been made outside Japan.
The plant produced 475,000 vehicles last year - 80% of which were exported.
Production of the next Qashqai model is expected to begin in 2018 or 2019.
There was "no cheque book" involved in the assurances given to Nissan ahead of its decision to boost UK production, Business Secretary Greg Clark has said.