Lowell said Kushner has been voluntarily cooperating with Mueller's investigation into Russian interference in the 2016 election.
Kushner has had two interview sessions with the Special Counsel's team. The first set of questions in November centered largely around former national security adviser Michael Flynn, according to the person familiar with the matter.
Then, in mid-April, Kushner sat for six to seven hours of questions that covered many topics, including his work on the Trump campaign, the transition and in the White House and about Trump's decision in May 2017 to fire Comey, the person said.
The Special Counsel's questioning focused only on Kushner's work with Trump and did not include topics such as Kushner's personal finances or those of his family business, Kushner Companies, according to the person.
Lowell said that Kushner last year became "one of the first to voluntarily cooperate with any investigation into the 2016 campaign and related topics."
"Since then, he has continued this complete cooperation, providing a large number of documents and sitting for hours of interviews with congressional committees and providing numerous documents and sitting for two interviews with the office of special counsel," Lowell said. "In each occasion, he answered all questions asked and did whatever he could to expedite the conclusion of all the investigations."
In February, Kushner's interim security clearance was downgraded from top secret to the far less sensitive "secret" level amid reports that foreign governments had been overheard discussing how easily they felt they could manipulate him, in part because of his financial debts.
The granting of the security clearance suggests that investigators' scrutiny of Kushner has decreased significantly. Current and former law enforcement officials said it would be very unusual for someone to get a full security clearance if there were an ongoing criminal investigation which had the potential to result in charges against that person.
Kushner's family business is finalising a deal to finance its most troubled Manhattan property, 666 Fifth Avenue, which faces a deadline early next year for repayment of a US$1.2 billion debt. Brookfield Asset Management, a Canadian real estate firm, said earlier this month that it had reached an agreement to invest in the property.
Mark Zaid, a national security lawyer, said people who lose their interim security clearances are often able to get their clearances restored after a fuller investigation of the issues that caused concern for security officers. He said career staff at the White House and in an intelligence agency, typically the CIA, generally make the decisions about restoring a clearance.
Zaid said he presumed Kushner received a permanent top-secret clearance with access to secure compartmented information - the clearance access usually needed to review the highly classified intelligence presented each day in the President's Daily Brief.
"For that job, he would normally need top secret and SCI," Zaid said.
The person familiar with the matter confirmed that Kushner was granted a top-secret clearance.
Kushner's months-long inability to get a permanent security clearance had long vexed the Administration, so much so that some officials felt unwilling to push the issue with others in similar straits. At one point, the White House had dozens of employees awaiting permanent clearances before Chief of Staff John Kelly ordered an overhaul of the process.
Some had expected Kushner might not receive a permanent clearance for the duration of Mueller's investigation. Even without a permanent clearance, the President's son-in-law had been allowed to see materials, including the President's Daily Brief, that are among the most sensitive in government.
