A statement from Celtic confirmed that former Scotland captain Brown had chosen “various charities and causes” that he wished to benefit from the proceeds, including relatives of former Celtic and Republic of Ireland midfielder Miller, who passed away last month after being diagnosed with cancer towards the end of last year.
Liverpool had been slated as possible opponents for the Celtic captain’s testimonial, but Jurgen Klopp’s side withdrew their availability.
Martin O’Neill, who led Celtic to three SPL titles, three Scottish Cups and one Scottish League Cup, as well as the UEFA Cup final in 2003, will return to Parkhead with an Irish select on May 20, the day after the Scottish Cup final.
Brown, whose 50 international caps earned him a spot in the SFA Hall of Fame, is on course to win an eighth Scottish title in his eleventh season with Celtic.
Hailing his influential club captain, Brendan Rodgers said: “When I became Celtic manager, I ensured one of my first jobs was to meet Scott, as we discussed our plans for the future.
“He is a hugely important figure at the club and someone who I have been privileged to work with.
“With a tremendous will to succeed in everything he does, he is someone who we know we can depend on, someone you want in your team and a man who has been the most influential player in Scottish football for some time.
“I know he is greatly appreciated by our supporters who see week in, week out, the energy, passion and commitment he gives to Celtic.
“Through his talent and ability he has been a major part of Celtic’s success, not only in my time but for many years.
“We will be delighted to take part in this match to honour a great man and a great Celtic captain.”