Chelsea and PSG both announced the deal in separate statements late Friday, but did not disclose financial details.
The British press is full of speculation as to his transfer fee, with it reported to be between 40 million pounds ($67 million) and 50 million pounds ($84 million) depending on incentives, which would be a record for a defender.
The move cannot be finalised until the start of the transfer window on June 10, but PSG said all sides wanted to reach an agreement “as soon as possible” so that Luiz can “prepare for and play in the World Cup in his home country in the best possible conditions.”
Chelsea said the Brazil international has passed a medical examination but still needs to finalise the personal terms of his contract with PSG.
PSG paid a reported 42 million euros in 2012 for Thiago Silva, who could now link up with his Brazil team mate in central defence.
Luiz’s arrival will also make up for the departure of Alex, another Brazil defender bought from Chelsea in 2012, who is out of contract.
Luiz has been one of the Premier League’s top defenders and free-kick takers over the past few seasons, and can also play as a defensive midfielder.
A shaggy-haired ‘monster’ defender
The shaggy-haired player, full name David Luiz Moreira Marinho, was a midfielder in his younger days in Sao Paulo before being converted to defence as a teenager with Vitoria.
He was still only 19 when he followed the well-trodden path from Brazil to Portugal in 2007, joining Benfica on loan and then permanently.
Portuguese League Player of the Year in 2009-10, he was rewarded with a step up from Brazil’s Under-20 side to the senior squad under Mano Menezes.
In January 2011 he joined Chelsea for a reported fee of 25 million euros ($34.08 million) plus midfielder Nemanja Matic.
Among his final matches for the London side were the two Champions League quarter-final ties against PSG last month.
Chelsea won the second leg 2-0 to go through on away goals, after which Mourinho singled out Luiz’s performance – in midfield – describing him as “a monster”.
An expensive monster perhaps, but one the Ligue 1 club will be delighted to have on their side.
He is expected to start for Brazil at this summer’s World Cup.