Mr Blair, currently an Anglican, is expected to be received into the church in a mass at the private chapel of Cardinal Cormac Murphy-O'Connor, the Archbishop of Westminster.
His wife, Cherie, and four children are Catholics and the family have worshipped together for years.
In one of his final acts as premier, Mr Blair met Pope Benedict and was believed to have told him of his determination to leave the Church of England.
The move was disclosed by the Catholic weekly The Tablet, which said the service would be held this month.
Mr Blair's spokesman did not deny the story, but said: "This is the same old speculation."
However, a friend said it was "not without substance".
His move will divide Catholics. As an MP Mr Blair voted for abortion at up to 24 weeks.
All four of the Blair children were baptised as Catholics and the whole family used to attend mass at St Joan of Arc Church in Islington, north London.
After becoming prime minister in 1997 he was told to stop taking Holy Communion by the late Cardinal Hume, then leader of Catholics in England and Wales.
He continued to attend private masses with Fr Michael Seed, a Westminster priest.