Former Delta State Governor James Ibori was convicted of money laundering in the UK in 2012.
He is thought to have stolen around £50m from the oil-rich state.
This is the first time that money recovered from criminals will be returned to Nigeria since an agreement was signed in 2016, the UK authorities say.
The UK and Nigerian governments signed an agreement on Tuesday that the £4.2m recovered by UK agencies would be sent back to Nigeria for infrastructure projects, including the Lagos to Ibadan Expressway, the Abuja to Kano road and the second Niger Bridge.
Ibori was governor of Delta state from 1999-2007. On February 27th, 2012, Ibori pleaded guilty to 10 counts of money laundering, fraud, conspiracy to defraud, and other offenses in a London court. He also pleaded guilty to stealing over $250 million public funds while he was governor.
But he was put in immigration detention and he sued the Home Office for unlawful detention.
A Home Office email, published in the court judgement, recommended to keep him in immigration detention to buy time to work out how to recover at least £57m.
