The former prime minister has been recalling his many meetings with the Queen ahead of her funeral on Monday.
He first met the Queen nearly four decades ago when she opened the Mossmorran chemical plant in Fife in 1986.
Mr Brown, a former Kirkcaldy and Cowdenbeath MP, would then attend regular audiences with the Queen as he presented the budget as Chancellor and later as Prime Minister from 2007 to 2010.
His tenure came during the severe global economic crisis which plunged Britain into recession.
She was diligent, dutiful, read all of the papers and never tried to tell you what to do, but was always ready to ask questions
Speaking on BBC Radio Scotland’s the Sunday Show, Mr Brown said: “She was very understanding of the problems that we all faced at the time of the global financial crisis.”
The late monarch, he said, volunteered to entertain world leaders at the G20 meeting in 2009 – as the effects of the crisis took hold.
During the meeting, the Queen put former Italian minister Silvio Berlusconi “in his place” for arriving late.
Mr Brown recalled: “We had this group photograph and she was at the centre. I was sitting next to her, Obama was there.
“Berlusconi rushes in late and shouts ‘Obama’ and wants to be the centre of attention – rushes right up to the Queen and Obama.
“And, of course, the sternest look, I have never seen anything like it. Berlusconi was certainly put in his place by the Queen.”
The former Labour leader also told how the Queen was always up to date with current affairs but never tried to “impose her will” on the elected Government.
He added: “She was diligent, dutiful, read all of the papers and never tried to tell you what to do, but was always ready to ask questions.
“She asked me ‘why did the bankers do so badly?’ because of the financial crisis but she would never impose her will.”
“I think the dignified role of the monarchy which Prince Charles has promised to uphold, has really been established in the way she dealt with the business of state, that she was there to listen,” he added.
“She was there to ask questions, but she wasn’t there to impose her will. That was for the elected parliament of the day.”