The 31-year-old died after being restrained by officers responding to a call in Kirkcaldy, Fife, on May 3 2015.
His family previously criticised the length of time taken to investigate his death with prosecutors still to decide whether or not there should be any criminal proceedings.
Family solicitor Aamer Anwar confirmed at the weekend that legal action is planned before time-barring rules come into effect on Thursday.
The family are understood to be seeking £2 million in damages.
Mr Anwar said no amount of money will bring Mr Bayoh back and the family want justice.
The civil action is believed to be the first of its kind in legal history in Scotland.
Mr Anwar will join My Bayoh’s partner Collette Bell and his sister Kadi Johnson to detail the legal action on Wednesday.
He said: “On May 3 it will be the three years since Sheku Bayoh was restrained by up to nine police officers and lost his life.
“Since then Sheku’s loved ones have waited for clarity as to the circumstances in which their beloved son, brother and partner died.
“Despite the passage of time, their pain remains raw and their grief made worse by the failure of the authorities to provide them with the answers they are entitled to.”
Mr Anwar added: “Now they have decided enough is enough and on Wednesday Sheku’s family will reveal the full details of the civil action, as well as the new demands they will now place on the Scottish Government and Crown Office.
“The family allege that Police Scotland’s officers failed in their duty of reasonable care to protect the life of Sheku Bayoh.
“No amount of money will bring Sheku Bayoh back - this, for the family, is about justice.”
Last week Police Scotland confirmed legal papers had been received from the family.