The Gunners also signed full-back Cedric Soares and center-back Pablo Mari to four-year contracts, Ornstein reports. Soares and Mari initially joined the club on loan from Southampton and Flamengo, respectively.
Luiz's contract was set to expire on June 30 and was a topic of discussion after Arsenal's 3-0 loss last week to Manchester City. The Brazilian was at fault for the first goal in the defeat, and he was sent off in the 49th minute for a challenge that resulted in a penalty.
Luiz took the blame for the result and chastised himself for taking so long to resolve his future.
Manager Mikel Arteta was keen on re-signing Luiz despite the series of errors, according to The Guardian's Nick Ames.
Luiz will now remain at Arsenal until the end of the 2020-21 season, when he'll be 34 years old.
Soares has yet to make an appearance for Arsenal since making the move to north London in January. The 28-year-old arrived with a knee injury and missed more time due to the coronavirus pandemic.
He was due to become a free agent at the end of his loan spell.
Mari, meanwhile, is expected to miss two or three months with an ankle sprain. The 26-year-old has made just two Premier League starts this season.