Both players are expected to be at Arsenal’s training ground in London Colney on Thursday to pass their medicals and sign their contracts.
Luiz will sign a two-year deal and will cost £8 million while Tierney will put pen to paper on a five-year contract. Celtic will receive £25m, which will be spread over the length of the deal.
Arsenal were actively looking for a centre-back following the departure of Laurent Koscielny, who left to join Bordeaux earlier in the transfer window, and looked at various options before the possibility of signing Luiz became available.
Raul Sanllehi, who is in charge of transfers at the club, concluded the deal with Chelsea after Luiz had fallen out with manager Frank Lampard at Stamford Bridge and refused to train with the first team on Wednesday.
Tierney, 22, has been a target for Arsenal all summer and the club were successful in their third bid for the player. Manager Unai Emery is a big fan of Tierney, who can also play as a left-sided centre-back, which was important for Emery.
In two spells with Chelsea, Luiz has won a Premier League title, as well two FA Cup, League Cup and Europa League triumphs and the Champions League in 2012.
He has also won titles in Portugal with Benfica and in France with Paris Saint-Germain, who he joined for £50 million from Chelsea in 2014 — a deal which made him the most expensive defender in the world at the time.
Tierney arrives at Arsenal having won five consecutive league titles at Celtic. He made his debut for the club as a 17-year-old in 2015 and has experience playing in the Champions League and Europa League from his time in Scotland.
Tierney missed Celtic’s Champions League qualifier against FC Cluj in Romania on Wednesday due to injury but flew to London after the match once Arsenal agreed terms with the Scottish champions.
The left-back was ruled out of Celtic’s preseason due to a hip injury, which also caused Tierney to miss a large part of Celtic’s Treble winning season last campaign. Celtic manager Neil Lennon said on Wednesday that the full-back is expected to return to full fitness in a couple of weeks.
Luiz and Tierney will look to improve a defensive unit which conceded 51 Premier League goals last season.